Skills · Linear Equations · Systems of Equations
Systems: substitution
Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.
Problem types
- one equation solved for y: y = 2x + 1 and 3x + 2y = 16
- one equation solved for x: x = 3y − 2 and 2x + y = 10
- no solution (parallel lines): y = 2x + 1 and −6x + 3y = 5
- infinitely many solutions (same line): y = 2x + 1 and −6x + 3y = 3
Sample Sheet · Level 1
- 4x + 2y = 34
y = x − 1 - y = x − 2
x + 3y = 14 - y = 2x − 4
x + y = 11 - x + y = 7
y = 2x + 1 - y = 2x − 2
x + 4y = 28 - y = x − 4
4x + y = 21 - y = 2x − 5
4x + y = 13 - 4x + 3y = 26
y = 3x − 13
Answer key
- (6, 5)
- (5, 3)
- (5, 6)
- (2, 5)
- (4, 6)
- (5, 1)
- (3, 1)
- (5, 2)
Sample Sheet · Level 3
- 4x + y = −20
y = x − 10 - x = −2y + 31
6x + 2y = 66 - −3x − y = 26
x = −2y − 22 - y = 4x + 33
−5x + 5y = 75 - y = −4x + 28
6x + y = 38 - x = −3y − 7
2x + 6y = −14 - y = −x − 3
−2x − 2y = 5 - x = 4y + 19
−3x − 7y = −19
Answer key
- (−2, −12)
- (7, 12)
- (−6, −8)
- (−6, 9)
- (5, 8)
- infinitely many solutions
- no solution
- (11, −2)
Make your own
Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.