Step 1) Solve the second equation for x:
x + y = 6
x + y - color(red)(y) = 6 - color(red)(y)
x + 0 = 6 - y
x = 6 - y
Step 2) Substitute (6 - y) for x in the first equation and solve for y:
x^2 + y^2 = 20 becomes:
(6 - y)^2 + y^2 = 20
36 - 12y + y^2 + y^2 = 20
1y^2 + 1y^2 - 12y + 36 = 20
(1 + 1)y^2 - 12y + 36 = 20
2y^2 - 12y + 36 = 20
2y^2 - 12y + 36 - color(red)(20) = 20 - color(red)(20)
2y^2 - 12y + 16 = 0
(2y - 8)(y - 2) = 0
Solution 1 for y:
2y - 8 = 0
2y - 8 + color(red)(8) = 0 + color(red)(8)
2y - 0 = 8
2y = 8
(2y)/color(red)(2) = 8/color(red)(2)
(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 4
y = 4
Solution 2 for y:
y - 2 = 0
y - 2 + color(red)(2) = 0 + color(red)(2)
y - 0 = 2
y = 2
Step 3) Substitute the values for y into the solution to the second equation at the end of Step 1 and calculate x:
x = 6 - y and x = 6 - y becomes:
x = 6 - 4 and x = 6 - 2
x = 2 and x = 4
The Solutions Are:
x = 2 and y = 4 or (2, 4)
AND
x = 4 and y = 2 or (4, 2)
