Question

Look at the system of equations below.

{y = − 2 x + 3
4 x − 3y = 11
What is the solution to the system? Show your work.

Answer 1

Answer:

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

$x=2,\:y=-1$

Step-by-step explanation:

Considering the system of the equation

$\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}$

$\mathrm{Subsititute\:}y=-2x+3$

$\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11$

$4x-3\left(-2x+3\right)=11$

$4x+6x-9=11$

$10x-9=11$

$10x-9+9=11+9$

$10x=20$

$x=2$

$\mathrm{For\:}y=-2x+3$

$\mathrm{Subsititute\:}x=2$

$y=-2\cdot \:2+3$

$y=-1$

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

$x=2,\:y=-1$