Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `x + 3y = -3`, `2x – y = 8`?

Answer 1

The point of intersection is: `(x,y)=(3, -2)`
The system is consistent as there is a shared point.

Explanation:

Consider `x+3y=-3`

Point `P_1` is on the x-axis at `y=0 => x+0=-3`
`color(white)("dddddddddddddddddddd")P_1->(x_1,y_1)=(-3,0)`

Point `P_2` the y-axis at `x=0 => 3y=-3 =>y=-1`
`color(white)("dddddddddddddddddddd")P_2->(x_2,y_2)=(0,-1)`

Draw a strait line through `P_1 and P_2` and continue to the edge of the graphing area.
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Consider `2x-y=8`

Point `P_3` is on the x-axis at `y=0 => 2x=8 => x=4`
`color(white)("dddddddddddddddddddd") P_3->(x_3,y_3)=(4,0)`

Point `P_4` is on the y-axis at `x=0 => -y=8 => y=-8`
`color(white)("dddddddddddddddddddd")P_4->(x_4.y_4)=(0,-8)`

Draw a strait line through `P_3 and P_4` and continue to the edge of the graphing area.