Question

What system of equations is shown on the graph below?

x - 2y = -4 and 2x + y =4
x - 2y = 4 and 2x + y = 4
x - 2y = -2 and 2x + y = -4
x - 2y = 2 and 2x + y =4

Answer 1

The answer is B.

Hope it helps

Answer 2

x - 2y = 4 and 2x + y = -4

Explanation:

Look at the picture.

Read the coordinates of intercepts of each line.

Put them to slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept → (0, b)

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

The blue line:

(4, 0), (0, -2) → b= -2

`m=(-2-0)/(0-4)=(-2)/(-4)=(2)/(4)=(2:2)/(4:2)=(1)/(2)`

Substitute the values of a slope and an y-intercept to the equation of a line:

`y=(1)/(2)x-2`

Convert to the standard form
`Ax+By=C`:

`y=(1)/(2)x-2` multiply both sides by 2

`2y=x-4` subtract x from both sides

`-x+2y=-4` change the signs

`x-2y=4`

The red line:

(-2, 0), (0, -4) → b= -4

`m=(-4-0)/(0-(-2))=(-4)/(2)=-2`

`y=-2x-4` add 2x to both sides

`2x+y=-4`