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Help math
look at pic​

Help math look at pic​-example-1
User Ruprit
by
8.6k points

1 Answer

4 votes

Answer:
\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}

Explanation:

Given the system of equation


1)~y=-(x+2)^2+1


2)~y=2x+5

Expand the parenthesis of the 1) equation


y=-(x+2)^2+1


y=-(x^2+4x+4)+1


y=-x^2-4x-4+1


y=-x^2-4x-3

Current System


1)~y=-x^2-4x-3


2)~y=2x+5

Substitute the y value of the 1) equation with the 2) equation


2x+5=-x^2-4x-3

Add ( x² + 4x + 3) on both sides


2x+5+(x^2+4x+3)=-x^2-4x-3+(x^2+4x+3)


2x+5+x^2+4x+3=0

Combine like terms


x^2+2x+4x+5+3=0


x^2+6x+8=0

Factorize the quadratic equation


(x+4)(x+2)=0


x=-4~\text{or}~x=-2

Substitute the x values into one of the equations to find the y value


y=2x+5


y=2(-4)+5=-8+5=-3


y=2(-2)+5=-4+5=1

Therefore, the two solutions are:


\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}

Hope this helps!! :)

Please let me know if you have any questions

User Yur Gasparyan
by
8.6k points

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