Question

SOLVING EACH SYSTEM BY ELIMINATION x+3y=5 x=-6y+14 HELP

Answer 1

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=-4,\:y=3$

Step-by-step explanation:

Given the system of the equations

$x+3y=5;\:x=-6y+14$

solving by elimination method

$\begin{bmatrix}x+3y=5\\ x=-6y+14\end{bmatrix}$

$\mathrm{Arrange\:equation\:variables\:for\:elimination}$

$\begin{bmatrix}x+3y=5\\ x+6y=14\end{bmatrix}$

$x+6y=14$

$-$

$\underline{x+3y=5}$

$3y=9$

$\begin{bmatrix}x+3y=5\\ 3y=9\end{bmatrix}$

solve $3y=9$ for $y$:

$3y=9$

$\frac{3y}{3}=\frac{9}{3}$

$y=3$

$\mathrm{For\:}x+3y=5\mathrm{\:plug\:in\:}y=3$

Solve $x+3\cdot \:3=5$ for x:

$x+3\cdot \:3=5$

$x+9=5$

$x=-4$

Therefore,

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=-4,\:y=3$