Question

solve the system by Substitution 4x+4y=-4 y=-7x-7

Answer 1

x= -1,

y=0

Explanation:

`\begin{bmatrix}4x+4y=-4\\ y=-7x-7\end{bmatrix}\\\\\mathrm{Subsititute\:}y=-7x-7\\\\\begin{bmatrix}4x+4\left(-7x-7\right)=-4\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}-24x-28=-4\end{bmatrix}\\\\Isolate\:x \:for \:-24x-28=-4\:\::x =-1\\\\\mathrm{For\:}y=-7x-7\\\\\mathrm{Subsititute\:}x=-1\\\\y=-7\left(-1\right)-7\\\\-7\left(-1\right)-7 =0\\\\y=0\\\\\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\\x=-1,\:y=0`

Answer 2

Answer: {-1, 0}

Explanation: Since y = -7x - 7, we can replace the y in our first equation with

a -7x - 7 and our first equation now reads 4x + 4(-7x - 7) = -4.

To solve this equation, first distribute the 4 through the parenthses.

So we have 4x - 28x - 28 = -4.

Now simplify the left side to get -24x - 28 = -4.

Adding 28 to both sides, we have -24x = 24.

Dividing both sides by -24, we find that x = -1.

To find y, plug a -1 back into either equation.

So we have y = -7(-1) - 7 or y = 0.

Our final answer is {-1, 0}.