4. Systems of two equations

Solving two linear equations in two unknowns. Set for OMPT-A, OMPT-B, OMPT-D, OMPT-E and OMPT-G.

All OMPT worksheets

Questions

Sheet length

1

Solve the system and give the value of $x$ : $4 x + 2y = 20$ and $x -4y = -22$

Answer:

2

Solve the system and give the value of $x$ : $y = 2 - 2 x$ and $2 x + 2 y = 2$

Answer:

3

Solve the system and give the value of $x$ : $6 x + 3y = 18$ and $2 x -2y = -12$

Answer:

4

Solve the system and give the value of $x$ : $y = 3 x + 12$ and $x + 5 y = -4$

Answer:

5

Solve the system and give the value of $x$ : $x + 6y = -41$ and $3 x -5y = 38$

Answer:

6

Solve the system and give the value of $x$ : $y = 2 x + 10$ and $4 x + 3 y = -10$

Answer:

7

Solve the system and give the value of $x$ : $6 x + 4y = 2$ and $3 x -6y = -15$

Answer:

8

Solve the system and give the value of $x$ : $y = 2 x + 2$ and $4 x + 3 y = -4$

Answer:

9

Solve the system and give the value of $x$ : $5 x + 1y = 25$ and $5 x -1y = 15$

Answer:

10

Solve the system and give the value of $x$ : $y = 2 x + 4$ and $2 x + 3 y = -28$

Answer:

11

Solve the system and give the value of $x$ : $x + 4y = 1$ and $x -5y = 1$

Answer:

12

Solve the system and give the value of $x$ : $y = - 3 x - 14$ and $3 x + 2 y = -13$

Answer:

13

Solve the system and give the value of $x$ : $5 x + 4y = -13$ and $6 x -3y = -39$

Answer:

14

Solve the system and give the value of $x$ : $y = x + 1$ and $2 x + 3 y = 3$

Answer:

15

Solve the system and give the value of $x$ : $4 x + 4y = -12$ and $4 x -1y = -12$

Answer:

16

Solve the system and give the value of $x$ : $y = 4 x - 3$ and $5 x + 4 y = 30$

Answer:

17

Solve the system and give the value of $x$ : $3 x + 3y = -6$ and $2 x -4y = 38$

Answer:

18

Solve the system and give the value of $x$ : $y = 3 x + 6$ and $3 x + 5 y = 12$

Answer:

19

Solve the system and give the value of $x$ : $5 x + 2y = -12$ and $6 x -5y = -7$

Answer:

20

Solve the system and give the value of $x$ : $y = 9 - 4 x$ and $2 x + y = 7$

Answer:

21

Solve the system and give the value of $x$ : $x + 4y = 6$ and $6 x -6y = -24$

Answer:

22

Solve the system and give the value of $x$ : $y = - 4 x - 6$ and $5 x + 3 y = -18$

Answer:

23

Solve the system and give the value of $x$ : $3 x + 6y = -45$ and $6 x -3y = 0$

Answer:

24

Solve the system and give the value of $x$ : $y = - 3 x$ and $5 x + 3 y = 8$

Answer:

25

Solve the system and give the value of $x$ : $2 x + 2y = 6$ and $5 x -2y = -13$

Answer:

26

Solve the system and give the value of $x$ : $y = 19 - 4 x$ and $4 x + 2 y = 14$

Answer:

27

Solve the system and give the value of $x$ : $4 x + 3y = 12$ and $5 x -6y = 54$

Answer:

28

Solve the system and give the value of $x$ : $y = 2 x + 8$ and $5 x + 5 y = -50$

Answer:

29

Solve the system and give the value of $x$ : $6 x + 6y = 12$ and $3 x -6y = 33$

Answer:

30

Solve the system and give the value of $x$ : $y = 8 - 2 x$ and $5 x + 3 y = 21$

Answer:

Answers

Every answer below was re-derived independently before this page was built.

1

Answer: $2$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 2$ , $y = 6$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $6$

2

Answer: $1$

The first equation already gives $y$ , so put it straight into the second: $2x + 2\left(2 - 2 x\right) = 2$ . That leaves one unknown, and $x = 1$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $0$
Substituted into the equation it came from, which says nothing → $3$

3

Answer: $0$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 0$ , $y = 6$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $6$

4

Answer: $-4$

The first equation already gives $y$ , so put it straight into the second: $1x + 5\left(3 x + 12\right) = -4$ . That leaves one unknown, and $x = -4$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $0$
Substituted into the equation it came from, which says nothing → $1$

5

Answer: $1$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 1$ , $y = -7$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $-7$

6

Answer: $-4$

The first equation already gives $y$ , so put it straight into the second: $4x + 3\left(2 x + 10\right) = -10$ . That leaves one unknown, and $x = -4$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $2$
Substituted into the equation it came from, which says nothing → $-1$

7

Answer: $-1$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -1$ , $y = 2$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $2$

8

Answer: $-1$

The first equation already gives $y$ , so put it straight into the second: $4x + 3\left(2 x + 2\right) = -4$ . That leaves one unknown, and $x = -1$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $0$
Substituted into the equation it came from, which says nothing → $2$

9

Answer: $4$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 4$ , $y = 5$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $5$

10

Answer: $-5$

The first equation already gives $y$ , so put it straight into the second: $2x + 3\left(2 x + 4\right) = -28$ . That leaves one unknown, and $x = -5$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $-6$
Substituted into the equation it came from, which says nothing → $-2$

11

Answer: $1$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 1$ , $y = 0$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $0$

12

Answer: $-5$

The first equation already gives $y$ , so put it straight into the second: $3x + 2\left(- 3 x - 14\right) = -13$ . That leaves one unknown, and $x = -5$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $1$
Substituted into the equation it came from, which says nothing → $-3$

13

Answer: $-5$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -5$ , $y = 3$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $3$

14

Answer: $0$

The first equation already gives $y$ , so put it straight into the second: $2x + 3\left(x + 1\right) = 3$ . That leaves one unknown, and $x = 0$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $1$
Substituted into the equation it came from, which says nothing → $3$

15

Answer: $-3$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -3$ , $y = 0$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $0$

16

Answer: $2$

The first equation already gives $y$ , so put it straight into the second: $5x + 4\left(4 x - 3\right) = 30$ . That leaves one unknown, and $x = 2$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $5$
Substituted into the equation it came from, which says nothing → $6$

17

Answer: $5$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 5$ , $y = -7$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $-7$

18

Answer: $-1$

The first equation already gives $y$ , so put it straight into the second: $3x + 5\left(3 x + 6\right) = 12$ . That leaves one unknown, and $x = -1$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $3$
Substituted into the equation it came from, which says nothing → $4$

19

Answer: $-2$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -2$ , $y = -1$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $-1$

20

Answer: $1$

The first equation already gives $y$ , so put it straight into the second: $2x + 1\left(9 - 4 x\right) = 7$ . That leaves one unknown, and $x = 1$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $5$
Substituted into the equation it came from, which says nothing → $2$

21

Answer: $-2$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -2$ , $y = 2$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $2$

22

Answer: $0$

The first equation already gives $y$ , so put it straight into the second: $5x + 3\left(- 4 x - 6\right) = -18$ . That leaves one unknown, and $x = 0$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $-6$
Substituted into the equation it came from, which says nothing → $3$

23

Answer: $-3$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -3$ , $y = -6$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $-6$

24

Answer: $-2$

The first equation already gives $y$ , so put it straight into the second: $5x + 3\left(- 3 x\right) = 8$ . That leaves one unknown, and $x = -2$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $6$
Substituted into the equation it came from, which says nothing → $1$

25

Answer: $-1$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = -1$ , $y = 4$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $4$

26

Answer: $6$

The first equation already gives $y$ , so put it straight into the second: $4x + 2\left(19 - 4 x\right) = 14$ . That leaves one unknown, and $x = 6$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $-5$
Substituted into the equation it came from, which says nothing → $8$

27

Answer: $6$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 6$ , $y = -4$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $-4$

28

Answer: $-6$

The first equation already gives $y$ , so put it straight into the second: $5x + 5\left(2 x + 8\right) = -50$ . That leaves one unknown, and $x = -6$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $-4$
Substituted into the equation it came from, which says nothing → $-1$

29

Answer: $5$

Eliminate $y$ by scaling and adding, or substitute. The solution is $x = 5$ , $y = -3$ .

Common mistakes, and the answer each one gives:

Solved for y instead of x → $-3$

30

Answer: $3$

The first equation already gives $y$ , so put it straight into the second: $5x + 3\left(8 - 2 x\right) = 21$ . That leaves one unknown, and $x = 3$ .

Common mistakes, and the answer each one gives:

Gave the value of $y$ rather than of $x$ → $2$
Substituted into the equation it came from, which says nothing → $6$