Question

solve the following system using substitution: -7x - 2y = -13; x = 2y + 11. options: (-3, 4); (3, 4); (3, -4); (-3, -4)

Explanation:

Step1: Substitute $x=2y+11$ into first equation

$-7(2y + 11) - 2y = -13$

Step2: Expand and simplify left side

$-14y - 77 - 2y = -13$
$-16y - 77 = -13$

Step3: Isolate the term with $y$

$-16y = -13 + 77$
$-16y = 64$

Step4: Solve for $y$

$y = \frac{64}{-16} = -4$

Step5: Substitute $y=-4$ into $x=2y+11$

$x = 2(-4) + 11 = -8 + 11 = 3$

Answer:

C. $(3, -4)$