Question

algebra i(h)-4
4-2 mathxl 12 problems
solve the system of equations by the substitution method.
$\begin{cases} x + 11y = 40\\2x + 5y = 12 end{cases}$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is . (simplify your answer. type an ordered pair)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Isolate x from first equation

$x = 40 - 11y$

Step2: Substitute x into second equation

$2(40 - 11y) + 5y = 12$

Step3: Simplify and solve for y

$80 - 22y + 5y = 12$
$80 - 17y = 12$
$-17y = 12 - 80$
$-17y = -68$
$y = \frac{-68}{-17} = 4$

Step4: Substitute y=4 into x's equation

$x = 40 - 11(4) = 40 - 44 = -4$

Answer:

A. The solution is $(-4, 4)$