Question

practice exercises lesson 7.3b
solve the system of equation using the addition/elimination method.
$3x + 2y = 14$
$3x - 2y = 10$
\\(\bigcirc\\) (6, -2)
\\(\bigcirc\\) (4, 1)
\\(\bigcirc\\) (0, 7)
\\(\bigcirc\\) (2, -2)

Explanation:

Step1: Add the two equations

Add the equations \(3x + 2y = 14\) and \(3x - 2y = 10\) together. The \(y\)-terms will eliminate:

$$
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$$

Step2: Solve for \(x\)

Divide both sides of \(6x = 24\) by 6:

$$ x = \frac{24}{6} = 4 $$

Step3: Substitute \(x = 4\) into one of the original equations

Let's use the first equation \(3x + 2y = 14\). Substitute \(x = 4\):

$$ 3(4) + 2y = 14\\ 12 + 2y = 14 $$

Step4: Solve for \(y\)

Subtract 12 from both sides:

$$ 2y = 14 - 12\\ 2y = 2 $$

Divide both sides by 2:

$$ y = \frac{2}{2} = 1 $$

So the solution to the system is \((4, 1)\).

Answer:

(4, 1)