Question

1. -2x + 12y = 18

4x - 2y = 30

Explanation:

We have a system of linear equations:

$$
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$$

We can use the elimination method. First, let's multiply the first equation by 2 to make the coefficients of \(x\) in both equations opposites (or to eliminate \(x\)).

Step 1: Multiply the first equation by 2

Multiply each term in \(-2x + 12y = 18\) by 2:

$$ 2\times(-2x)+2\times(12y)=2\times18 $$

$$ -4x + 24y = 36 $$

Step 2: Add the new first equation and the second equation

Now we have the two equations:

$$ -4x + 24y = 36 $$

$$ 4x - 2y = 30 $$

Add them together:

$$ (-4x + 4x)+(24y - 2y)=36 + 30 $$

Simplify:

$$ 22y = 66 $$

Step 3: Solve for \(y\)

Divide both sides of \(22y = 66\) by 22:

$$ y=\frac{66}{22}=3 $$

Step 4: Substitute \(y = 3\) into one of the original equations to solve for \(x\)

Let's use the second equation \(4x - 2y = 30\). Substitute \(y = 3\):

$$ 4x - 2\times3 = 30 $$

$$ 4x - 6 = 30 $$

Add 6 to both sides:

$$ 4x=30 + 6 $$

$$ 4x=36 $$

Divide both sides by 4:

$$ x=\frac{36}{4}=9 $$

Answer:

The solution to the system of equations is \(x = 9\) and \(y = 3\), or as an ordered pair \((9, 3)\).