Question

solve the system of equations by the substitution method.
$x = 2y - 9$
$x = 4y - 3$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Substitute x from first equation

Set $2y - 9 = 4y - 3$

Step2: Isolate y terms

$-9 + 3 = 4y - 2y$
$\implies -6 = 2y$

Step3: Solve for y

$y = \frac{-6}{2} = -3$

Step4: Substitute y to find x

$x = 2(-3) - 9 = -6 - 9 = -15$

Answer:

A. The solution set is $\{(-15, -3)\}$.