The solutions set of the system of equations y=-x^2-2x+8 and y=2x+11 are as x = -3 , -1 and y = 5, 8.
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The system of equations
[tex]y = -x^2 - 2x + 8[/tex]
and
y = 2x + 11,
We can put the value of y in the first equation
[tex]y = -x^2 - 2x + 8\\\\2x+11 = -x^2 - 2x + 8\\\\2x + 2x + 11 - 8 +x^2 = 0\\\\4x + 3 + x ^2 = 0[/tex]
The factors are;
[tex]x^2 +4x + 3 = 0\\\\(x+3)(x+ 1)[/tex]
Or x = -3 , -1
Now substitute to find y;
y = 2x + 11
y = 2(-1) + 11
y = 8
y = 2x + 11
y = 2(-3) + 11
y = 5
Or y = 5, 8
Thus, the solutions set of the system of equations y=-x^2-2x+8 and y=2x+11 are as x = -3 , -1 and y = 5, 8.
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