Question

David wants to find the solutions of this system of equations:
–4x – 7 = y x2
– 2x – 6 = y

Which statement is true?
There are no real number solutions.
There is one unique real number solution at (–1, –3).
There is one unique real number solution at (1, –3).
There are two real number solutions at (–1, –3) and (1, –7).

Answer 1

Your answer would be the second one. "There is one unique real number solution at (–1, –3)."

Answer 2

Solutions to the given system of equations are x= -1 and y=-4.

Given equations are:

$-4x-7=y+x^{2}$.....(1)

$-2x-6=y$........(2)

What is an equation?

An equation is a statement that equates to two expressions.

Rearranging the equation (1)

$y=-x^{2} -4x-7$

$y=-2x-6$

So, $-x^{2} -4x-7=-2x-6$

$x^{2} +2x+1=0$

$(x+1)^2=0$

$x+1=0$

$x=-1$

So, $y=-2*(-1)-6$

$y=-4$

Thus, solutions to the given system of equations are x= -1 and y=-4.

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