Question

6 from unit 2, lesson 15 solve this system of linear equations without graphing: \

$$\begin{cases}7x + 11y = -2 \\\\ 7x + 3y = 30\\end{cases}$$

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases}7x + 11y=-2\\7x + 3y = 30\end{cases}$$

Subtract the second equation from the first equation to eliminate \(x\):
$$(7x + 11y)-(7x + 3y)=-2 - 30$$
Simplify the left - hand side: \(7x+11y - 7x - 3y=8y\)
Simplify the right - hand side: \(-2-30=-32\)
So we get the equation \(8y=-32\)

Step2: Solve for \(y\)

From \(8y = - 32\), divide both sides by 8:
\(y=\frac{-32}{8}=-4\)

Step3: Substitute \(y = - 4\) into one of the original equations to solve for \(x\)

Substitute \(y=-4\) into the second equation \(7x + 3y=30\):
\(7x+3\times(-4)=30\)
Simplify: \(7x-12 = 30\)
Add 12 to both sides: \(7x=30 + 12=42\)
Divide both sides by 7: \(x=\frac{42}{7}=6\)

Answer:

The solution to the system of linear equations is \(x = 6\) and \(y=-4\), or the ordered pair \((6,-4)\)