# Solving systems of equations worksheets

 Name: ______________________ Date: __________________________

Find the solution for each system below by elimination or by substitution.

 1.y = 2x - 3y = x - 1x = ________   y = ___________ 2.y  =  -2x + 1y = 2x - 3x = ________   y = ___________

 3.4x - 2y = 82x + 2y = 4x = ________   y = ___________ 4.-2x - y = -22x + 4y = 11x = ________   y = ___________

 5.6x + 2y = 103x + 3y = -13x = ________   y = ___________ 6.7x - 12y = -135x + 4y = 19x = ________   y = ___________

 7.4x + 2y = 147x - 3y = -8x = ________   y = ___________ 8.15x + 3y = 910x + 7y = -4x = ________   y = ___________

 Name: _______________________ Date : _______________________

Tell whether the system below has 1 solution, no solution, or infinitely many solutions. If the system has a solution, find it.

 1. y = 6x + 1y = 6x - 1________________ 2. y = 3x + 1y = 2x - 1________________

 3. y = -5x + 1y = -5x + 1________________ 4. y = 8x - 5y = -8x - 5________________

 5. 2y - 6x = 10 2y + 6x = -10________________ 6. 10y = 20x + 4010y = 20x + 10________________

 7. y = (1/5)x - 2 5y + 10 = x________________ 8. y = (1/4)x + 6 4y - 24 = -x________________

## Solving systems of equations worksheets: a few things to keep in mind and/or remember.

What is solving by the substitution method?

You can solve by substitution when you plug in either the value of x or the value of y into one of the two equations.

Example:

x = y + 1

y + x = 21

Here, you can just replace the value of x or y + 1 in y + x = 21

y + y + 1 = 21

2y + 1 = 21

2y = 20

y = 10 and x  = y + 1 = 10 + 1 = 11

What is solving by elimination method?

You can solve by elimination when you eliminate either x or y by adding the two equations. We may need to rewrite one or both equations!

Example:

x = y + 1

y + x = 21

Let us rewrite x = y + 1 as x - y = 1 and then add the two equations to eliminate y.

x - y = 1

y + x = 21

Let us add the two equations.

2x - y + y = 1 + 21

2x + 0 = 22

2x = 22

x = 11

Using y + x = 21, y + 11 = 21, so y = 21 - 11 = 10.

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