Solve the system of equations: y=x^2+3x-6 y=2x-6
2 answers:
Answer:
Solution: {(-1,-8), (0,-6)}
Step-by-step explanation:
y=x^2+3x-6 ............(1)
y=2x-6 ....................(2)
Solution:
by comparison, the right-hand sides of both equations are equal (to y)
x^2+3x-6 = 2x - 6
Transpose and simplify
x^2 -x = 0
x = -1 or x=0
Substitute x = -1 in (2)
y = 2(-1) -6 = -8 ..............(-1,-8)
substitute x = 0 in (2)
y = 2(0) -6 = -6 ...............(0,-6)
So there are two solutions, corresponding to the intersection of the quadratic and the straight line.
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