Answer:
Solutions ( 14 , 6) ( 4 , -4).
Explanation:
Given : y = x² − 3x − 4 and x = y + 8.
To find : What is the solution set of this system of equations.
Solution : We have given
y = x² − 3x − 4 ------(1)
x = y + 8 --------(2)
Plug the equation 2 in equation 1.
y = (y +2)² − 3( y + 8) − 4 .
y = y² + 4 + 2y - 3y - 24 - 4 .
y = y² - y + 4 - 24 - 4.
y = y² - y - 24
On subtracting both sides by y
y² - 2y - 24 = 0.
On factoring
y² - 6y + 4y - 24 = 0.
On taking common y from first two term and 4 from last two terms.
y ( y - 6) + 4 ( y - 6) = 0.
On grouping
(y -6) ( y + 4) = 0
For y - 6 = 0
y = 6
For y +4 = 0
y = -4.
Plug y =6 in equation 2
x = 6 + 8
x = 14.
Plug y = - 4 in equation 2.
x = -4 + 8
x = 4.
Solutions ( 14 , 6) ( 4 , -4).
Therefore, Solutions ( 14 , 6) ( 4 , -4).