Answer to Question #162128 in Algebra for Will

Question

Solve the system of equations:

y= x² - 6x +3

y= -2x -6

Answer 1

y=x²-6x+3

y=-2x-6

We equate the two equations as below;

x²-6x+3=-2x-6

Rearranging the above, we have;

x²-4x+9=0

We now solve the quadratic equation above.

The quadratic formula to be used is as below;

x=-b+- sqrt(b²-4ac)/2a

so;

x=-(-4)+- sqrt(-4²-4*1*9)/2*1

x=4)+- sqrt(-20)/2

x = 2 - 2.24i

or

x = 2 + 2.24i

Now using the above values of x to find the possible values of y using the second equation.

y=-2x-6

y=-2(2 - 2.24i)-6

y=-10 +4.48i

or

y=-2x-6

y=-2(2 + 2.24i)-6

y=-10 -4.48i