Question

Solve this system of equations: y = x2 – 3x + 12 y = –2x + 14 What are the solutions ?

Answer 1

Answer:
The solution to the system of equation would be the two order pairs (2,10) and (-1,16)

Explanation:
The solution means the value of x that satisfies both equations.
Therefore, we will equate the two equations given and solve for x.
The first is: y = x^2 - 3x + 12
The second is : y = -2x + 14
Equate both and solve for x as follows:
x^2 - 3x + 12 = -2x + 14
x^2 - 3x + 2x + 12 - 14 = 0
x^2 - x - 2 = 0
(x-2)(x+1) = 0
either x = 2 and y = (2)^2 - 3(2) + 12 = -2(2) + 14 = 10
or x = -1 and y = (-1)^2 - 3(-1) + 12 = -2(-1) + 14 = 16
Therefore, the solution to the system of equation would be the two order pairs (2,10) and (-1,16)

Hope this helps :)