Given the system of equations presented here:4x + y = 42x + 6y = 24Which action creates an equivalent system that will eliminate one variable when they are combined?A.Multiply the first equation by -4 to get -16x - 4y = -16.B.Multiply the second equation by -4 to get - 8x - 24y = -96.C.Multiply the first equation by -2 to get -8x - 2y = -8.D.Multiply the second equation by -2 to get - 4x - 12y = -48.
Accepted Solution
A:
Answer:D.Multiply the second equation by -2to get - 4x - 12y = -48.Step-by-step explanation:[tex]\left\{\begin{array}{ccc}4x+y=4\\2x+6y=24&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+y=4\\-4x-12y=-48\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad11y=-44\qquad\text{divide both sides by 11}\\.\qquad\qquad y=-4\\\\\text{put the value of y to the first equation:}\\\\4x+(-4)=4\\4x-4=4\qquad\text{add 4 to both sides}\\4x=8\qquad\text{divide both sides by 4}\\x=2[/tex]