Question

How do you solve the system of equations `y+ 7x = 3` and `y = x ^ { 2} + x - 6`?

Answer 1

Write the first equation in slope-intercept form.
Set the right sides of the two equations equal.
Solve for the two x values (if they are real)
Use the first equation to find the y values.

Explanation:

Write the first equation in slope-intercept form:

`y = -7x+3`

Set the right sides of the two equations equal.

`-7x+3=x^2+x-6`

Solve for the two x values (if they are real)

#x^2+8x-9=0

#(x-1)(x+9)=0

`x = 1 and x = -9`

Use the first equation to find the y values.

`y = -7(1)+3 = -4`

`y = -7(-9) + 3 = 66`

The solution points are `(1,-4) and (-9,66)`

Here is a graph of the two functions:

graph{(y+ 7x - 3)(x^2+x-6-y)=0 [-10, 10, -5, 5]}

You can find the two points intersection points.