Systems of Equations Practice
Find the x and y that make both equations true, by substitution or by elimination.
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Solve the system.
12 problems
- 1.x − y = 6; 2x + y = 15Answerx=7; y=1
Add equation 2
3×x=21; 2×x+y=15Move 3 to the other side
x=7; 2×x+y=15Eliminate x with equation 1
x=7; y=1
- 2.x + y = 3; x − y = 1Answery=1; x=2
Subtract equation 2
2×y=2; x−y=1Move 2 to the other side
y=1; x−y=1Add equation 1
y=1; x=2
- 3.x + y = 23; x − y = 5Answery=9; x=14
Subtract equation 2
2×y=18; x−y=5Move 2 to the other side
y=9; x−y=5Add equation 1
y=9; x=14
- 4.5x + y = 16; x − 2y = 1Answery=1; x=3
Eliminate x with equation 2
11×y=11; x−2×y=1Move 11 to the other side
y=1; x−2×y=1Eliminate y with equation 1
y=1; x=3
- 5.x − y = 3; 2x + y = 15Answerx=6; y=3
Add equation 2
3×x=18; 2×x+y=15Move 3 to the other side
x=6; 2×x+y=15Eliminate x with equation 1
x=6; y=3
- 6.x + y = 7; x − y = 1Answery=3; x=4
Subtract equation 2
2×y=6; x−y=1Move 2 to the other side
y=3; x−y=1Add equation 1
y=3; x=4
- 7.x + y = 12; x − y = 2Answery=5; x=7
Subtract equation 2
2×y=10; x−y=2Move 2 to the other side
y=5; x−y=2Add equation 1
y=5; x=7
- 8.y = 3x + 1; x + y = 13Answerx=3; y=10
Subtract equation 2
−x=3×x−12; x+y=13Move 3×x to the other side
−4×x=−12; x+y=13Move −4 to the other side
x=3; x+y=13Subtract equation 1
x=3; y=10
- 9.y = 6x + 1; y = −x − 6Answery=−5; x=−1
Eliminate x with equation 2
7×y=−35; y=−x−6Move 7 to the other side
y=−5; y=−x−6Subtract equation 1
y=−5; 0=−x−1Move −x to the other side
y=−5; x=−1
- 10.y = 5x + 1; x + y = 7Answerx=1; y=6
Subtract equation 2
−x=5×x−6; x+y=7Move 5×x to the other side
−6×x=−6; x+y=7Move −6 to the other side
x=1; x+y=7Subtract equation 1
x=1; y=6
- 11.y = 2x + 1; y = −x − 8Answery=−5; x=−3
Eliminate x with equation 2
3×y=−15; y=−x−8Move 3 to the other side
y=−5; y=−x−8Subtract equation 1
y=−5; 0=−x−3Move −x to the other side
y=−5; x=−3
- 12.y = 3x + 1; x + y = 5Answerx=1; y=4
Subtract equation 2
−x=3×x−4; x+y=5Move 3×x to the other side
−4×x=−4; x+y=5Move −4 to the other side
x=1; x+y=5Subtract equation 1
x=1; y=4
Substitution: solve one equation for a letter and put it into the other. Elimination: add the equations so one letter cancels.
Common questions
- Substitution or elimination?
- Substitution when a letter is already alone, elimination when one letter cancels by adding.
- How do I check the answer?
- Put x and y into both equations. Both must be true.
