Question

Question #b1d06

Answer 1

Substitute the right side of the second equation for y into the first equation.
Solve for the x coordinates
Use the second equation to find the corresponding y coordinates.

Explanation:

Given:

`x^2 + y^2 = 25" [1]"`
`y = x - 7" [2]"`

Substitute `x-7` for y into equation [1]:

`x^2 + (x-7)^2 = 25`

Expand the square:

`x^2 + x^2-14x+ 49 = 25`

Combine like terms:

`2x^2-14x+ 24 = 0`

Divide both sides by 2:

`x^2-7x+ 12 = 0`

Factor:

`(x - 3)(x - 4) = 0`

`x = 3` and `x = 4`

Use equation [2] to find the y coordinates:

`y = x - 7`

`y = 3 - 7` and `y = 4 - 7`

`y = -4` and `y = -3`

The points that solve the two equation are `(3,-4)` and `(4,-3)`

Here is a graph of the two equations:

graph{(x^2+y^2-25)(y-x+7)=0 [-10, 10, -5, 5]}