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Solving systems of equations by substitution worksheets Grade 8

Substitute one equation into the other, solve for x, then find y.

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How to do it

Put the expression for y into the other equation. Solve for x, then find y.

y=−3x−12;−3x−4y=−6x=−6,y=6y = -3x - 12;\quad -3x - 4y = -6\quad x = -6, y = 6
−3x−4(−3x−12)=−6-3x - 4(-3x - 12) = -6put −3x − 12 in for y
9x+48=−69x + 48 = -6distribute and combine
9x=−549x = -54
x=−6x = -6
y=(−3)(−6)+(−12)=6y = (-3)(-6) + (-12) = 6put x back in to find y

Example problems

  1. y=−3x−23;−3x−2y=28y = -3x - 23;\quad -3x - 2y = 28
  2. y=x+6;5x+y=−30y = x + 6;\quad 5x + y = -30
  3. y=−x−6;5x+y=−26y = -x - 6;\quad 5x + y = -26
  4. y=−2x−5;3x−y=−5y = -2x - 5;\quad 3x - y = -5

Linear equations and systems

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  6. Standard form to slope-intercept form
  7. Solving systems of equations by substitution
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