Question

Solve the system by elimination. 4x=−3y−10 9x+2y=6

Answer 1

Answer:

x = 2, y = -6

Step-by-step explanation:

$\left\{\begin{array}{ccc}4x=-3y-10&\text{add}\ 3y\ \text{to both sides}\\9x+2y=6\end{array}\right\\\\\left\{\begin{array}{ccc}4x+3y=-10&\text{multiply both sides by 2}\\9x+2y=6&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+6y=-20\\-27x-6y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-19x=-38\qquad\text{divide both sides by (-19)}\\.\qquad\dfrac{-19x}{-19}=\dfrac{-38}{-19}\\.\qquad \boxed{x=2}$

$\text{Put the value of}\ x\ \text{to the second equation:}\\\\9(2)+2y=6\\18+2y=6\qquad\text{subtract 18 from both sides}\\2y=-12\qquad\text{divide both sides by 2}\\\dfrac{2y}{2}=\dfrac{-12}{2}\\\boxed{y=-6}$