Question

Graph the system below and write its solution.1y=x+3- 2x + y = 6Note that you can also answer "No solution" or "Infinitely many" solutions.10+6-Solution:-10

Answer 1

EXPLANATION

The system of equations is given by the following expression:

(1) y = (1/2)x + 3

(2) -2x + y = 6

Substitute y= (1/2)x + 3

$\begin{bmatrix}-2x+\frac{1}{2}x+3=6\end{bmatrix}$

Simplifying:

$-2x+\frac{1}{2}x+3=6$

Adding similar elements:

$-\frac{3}{2}x+3=6$

Subtracting -3 to both sides:

$-\frac{3}{2}x=6-3$$\mathrm{Multiply\: both\: sides\: by\: }2$$2\mleft(-\frac{3}{2}x\mright)=3\cdot\: 2$

Simplify:

$-3x=6$

Divide both sides by -3:

$\frac{-3x}{-3}=\frac{6}{-3}$

Simplify:

$x=-2$$\mathrm{For\: }y=\mleft(\frac{1}{2}\mright)x+3$$\mathrm{Substitute\: }x=-2$$y=\frac{1}{2}\mleft(-2\mright)+3$

Remove parentheses: (-a) = -a

$=-\frac{1}{2}\cdot\: 2+3$$\frac{1}{2}\cdot\: 2$

Cancel the common factor:

$=1$$=-1+3$$\mathrm{Add/Subtract\: the\: numbers\colon}\: -1+3=2$

=2

y=2

$\mathrm{The\: solutions\: to\: the\: system\: of\: equations\: are\colon}$$y=2,\: x=-2$