Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `5x - y = -9` and `y + 2x = 2`?

Answer 1

`x=-1`
`y=4`

Explanation:

Determine the intercepts then connect the points to draw the lines.
For `5x-y=-9`
When `x=0`, `y=9`
`(0, 9)` is point on the line `5x-y=-9`

When `y=0`, `x=-9/5`
`(-9/5, 0)` is a point on the line `5x-y=-9`

Draw the line passing thru `(0, 9)` and `(-9/5, 0)`

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For `2x+y=2`
When `x=0`, `y=2`
`(0, 2)` is point on the line `2x+y=2`

When `y=0`, `x=1`
`(1, 0)` is a point on the line `2x+y=2`

Draw the line passing thru `(0, 2)` and `(1, 0)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~
The two lines intersect at `(-1, 4)`

The system is consistent.

Kindly see the graphs

God bless....I hope the explanation is useful.