Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `y = -3x - 7` and `-8x + 2y = 1`?

Answer 1

The solution is `(-15/14,-53/14)` or `~~(-1.07,-3.79)`. Since there is one solution, the system is consistent.

Explanation:

Equation 1: y=-3x-7#

Equation 2: -8x+2y=1#

Equation 1 is already solved for `y`. Substitute `-3x-7` for `y` in Equation 2 and solve for `x`.

`-8x+2(-3x-7)=1`

Expand.

`-8x-6x-14=1`

Add `14` to both sides.

`-8x-6x=1 +14`

Simplify.

`-14x=15`

Divide both sides by `-14`.

`x=-15/14` or `~~-1.07`

Substitute `-15/14` for `x` in Equation 1 and solve for `y`.

`y=-3(-15/14)-7`

Expand.

`y=45/14-7`

Multiply `7` by `14/14` to get an equivalent fraction with `14` as the denominator. Since `n/n=1`, the numbers will change, but not the value.

`y=45/14-(7xx14/14)`

Simplilfy.

`y=45/14-98/14`

Simplify.

`y=-53/14` or `~~3.79`

The solution is `(-15/14,-53/14)` or `~~(-1.07,-3.79)`. Since there is one solution, the system is consistent.

graph{(y+3x+7)(-8x+2y-1)=0 [-10, 10, -5, 5]}