Math Ladder
Sign inGet UnlimitedGet UnlimitedAccount

Solving systems of equations by elimination worksheets Grade 8

Multiply so one variable cancels, add the equations, and solve.

The front of the free solving systems of equations by elimination worksheet
Download PDFAnswer key

Free · Worked example · 8 problems · Answer key · US Letter

UnlimitedFresh versions and 5-sheet packetsGet Unlimited →

How to do it

Multiply so the y terms are opposites. Add the equations so y cancels.

4x+4y=32;x−3y=−12x=3,y=54x + 4y = 32;\quad x - 3y = -12\quad x = 3, y = 5
12x+12y=9612x + 12y = 96first equation × 3
4x−12y=−484x - 12y = -48second equation × 4
16x=4816x = 48add the equations: y cancels
x=3x = 3
12+4y=3212 + 4y = 32put x = 3 into the first equation
y=5y = 5

Example problems

  1. −3x+y=9;5x+3y=−29-3x + y = 9;\quad 5x + 3y = -29
  2. 2x−3y=27;5x+y=252x - 3y = 27;\quad 5x + y = 25
  3. −3x+y=0;5x+3y=14-3x + y = 0;\quad 5x + 3y = 14
  4. 5x−5y=0;x+3y=−245x - 5y = 0;\quad x + 3y = -24

Linear equations and systems

  1. Finding slope from two points
  2. Slope and y-intercept
  3. Slope and intercept from a graph
  4. Writing the equation of a line from a slope and a point
  5. Writing the equation of a line from two points
  6. Standard form to slope-intercept form
  7. Solving systems of equations by substitution
  8. Solving systems of equations by elimination