## Intermediate Algebra for College Students (7th Edition)

true for all values of $x$.
$y_{1}=2x + 6$ equation 1 $y_{2}=x + 8$ equation 2 $y_{3}=x$ equation 3 $3y_{1}-5y_{2} =y_{3}-22$ --> equation 4 Substitute equations 1 , 2 & 3 to equation 4: $3y_{1}-5y_{2} =y_{3}-22$ $3(2x + 6)-5(x + 8) =x-22$ Expand $3(2x + 6)$ = $6x+18$ Expand $5(x + 8)$ = $5x+40$ Rewrite the equation: $6x+18-(5x+40)=x-22$ $6x+18-5x-40=x-22$ $x-22=x-22$ Since both sides are equal, then the equation is true for all values of $x$.