Systems of Equations

Michigan State University - Diagnostic Exam

Which of the following are the x-coordinates of the solution to the system of equations, $7x - y = 25$ and $2 2 x + y = 25$ ?
a) 3 and 4 b) -3 and 4 c) 3 and -4

d) -3 and -4 e) $- 4 5$ and $--7 5$

Solution:

$7x-y= 25 ⇒ y = 7x - 25$

Substituting into the second equation yields

$x2+(7x - 25 )2 = 25 ⇒ 50x2 - 350x + 600 = 0 ⇒ 50(x - 4)(x - 3) = 0 ⇒ x = 3, 4$

Diagnostic:

If you miss this question please review nonlinear systems of equations and the method of substitution.

July 15, 2008