Question #b1d06

1 Answer
Apr 22, 2017

Answer:

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]}