Pearson Algebra 1 Common Core, 2011
PA
Pearson Algebra 1 Common Core, 2011 View details
3. Solving Systems Using Elimination
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Exercise 51 Page 384

Does either of the equations have an isolated variable in it?

(34,27)

Practice makes perfect

When solving a system of equations using substitution, there are three steps.

  1. Isolate a variable in one of the equations.
  2. Substitute the expression for that variable into the other equation and solve.
  3. Substitute this solution into one of the equations and solve for the value of the other variable.
For this exercise, y is already isolated in one equation, so we can skip straight to solving.
x-7=y & (I) 2x-y=41 & (II)
y=x-7 2x-y=41
y=x-7 2x-( x-7)=41
y=x-7 2x-x+7=41
y=x-7 x+7=41
y=x-7 x=34
Great! Now, to find the value of y, we need to substitute x for 34 into the first equation in the given system.
y=x-7 x=34
y= 34-7 x=34
y=27 x=34
The solution, or point of intersection, to this system of equations is the point (34,27).