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+(1)/(2)x+3=6\end{bmatrix}`

Simplifying:

`-2x+(1)/(2)x+3=6`

Adding similar elements:

`-(3)/(2)x+3=6`

Subtracting -3 to both sides:

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

Simplify:

`-3x=6`

Divide both sides by -3:

`(-3x)/(-3)=(6)/(-3)`

Simplify:

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

Remove parentheses: (-a) = -a

`=-(1)/(2)\cdot\: 2+3`
`(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`