Question

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$$\begin{cases} 10x + 5y = -25 \\\\ 4x + 4y = -12 \\end{cases}$$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(10x + 5y=-25\) by 5. We get \(2x + y=-5\), and then express \(y\) in terms of \(x\): \(y=-5 - 2x\).

Step2: Substitute into the second equation

Substitute \(y = - 5-2x\) into the second equation \(4x + 4y=-12\). So we have \(4x+4(-5 - 2x)=-12\). Expand the left - hand side: \(4x-20 - 8x=-12\). Combine like terms: \(-4x-20=-12\). Add 20 to both sides: \(-4x=-12 + 20=8\). Divide both sides by \(-4\): \(x=\frac{8}{-4}=-2\).

Step3: Find the value of y

Substitute \(x = - 2\) into \(y=-5 - 2x\). Then \(y=-5-2\times(-2)=-5 + 4=-1\).

Answer:

The solution of the system of equations is \(x=-2,y = - 1\)