Question

7x + 4y = -9
-7x - 3y = 12
(\boxed{ }, \boxed{ })
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Explanation:

Step1: Add the two equations

We have the system of equations:
\[

$$\begin{cases} 7x + 4y = -9 \\ -7x - 3y = 12 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively. The left - hand side: \((7x + 4y)+(-7x - 3y)=7x + 4y-7x - 3y=y\). The right - hand side: \(-9 + 12=3\). So we get \(y = 3\).

Step2: Substitute y into the first equation

Substitute \(y = 3\) into the equation \(7x+4y=-9\). We have \(7x+4\times3=-9\), that is \(7x + 12=-9\).

Step3: Solve for x

Subtract 12 from both sides of the equation \(7x+12=-9\): \(7x=-9 - 12=-21\). Then divide both sides by 7: \(x=\frac{-21}{7}=-3\).

Answer:

The solution of the system of equations is \(x=-3\), \(y = 3\), so the ordered pair is \((-3,3)\)