Skills · Linear Equations · Systems of Equations
Systems: elimination
Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.
Problem types
- opposite coefficients: add: 2x + y = 12 and 3x − y = 8
- same coefficients: subtract: 2x + 3y = 12 and 2x − y = 4
- multiply one equation first: 6x + 5y = 27 and 3x + y = 12
- multiply both equations first: 3x + 4y = 10 and 2x − 5y = 7
- no solution (parallel lines): 4x + 6y = 15 and 2x + 3y = 6
- infinitely many solutions (same line): x + 2y = 4 and 3x + 6y = 12
Sample Sheet · Level 1
- −2x + 4y = 12
2x + y = 13 - 4x − 2y = 0
x + 2y = 5 - 3x − 4y = −1
3x + 4y = 31 - 4x + 4y = 28
2x + 4y = 22 - x + 2y = 8
x + 3y = 11 - 2x − 3y = −3
4x + 3y = 39 - x + y = 6
x + 2y = 8 - 3x + y = 21
x + y = 9
Answer key
- (4, 5)
- (1, 2)
- (5, 4)
- (3, 4)
- (2, 3)
- (6, 5)
- (4, 2)
- (6, 3)
Sample Sheet · Level 3
- 7x + 7y = 49
7x + 5y = 55 - x + 6y = −71
x − 5y = 61 - x − 2y = −24
−6x + 2y = 84 - −15x + 12y = 313
−5x + 4y = 103 - 7x − 4y = −60
−5x + 3y = 42 - 2x − 10y = −28
5x + 5y = −40 - −4x − 10y = 44
−2x − 5y = 22 - −5x − 7y = 95
2x + 3y = −40
Answer key
- (10, −3)
- (1, −12)
- (−12, 6)
- no solution
- (−12, −6)
- (−9, 1)
- infinitely many solutions
- (−5, −10)
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.