Question

Solving with Elimination Practice
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Question
Solve the system of equations.
3x+6y=21

–5x+2y=13
(1 point)
(
,
)

Answer 1

To solve the system of equations using elimination, we start with the two equations:

1. \( 3x + 6y = 21 \) (Equation 1)
2. \( -5x + 2y = 13 \) (Equation 2)

**Step 1: Make the coefficients of y the same.**

To do this, we can multiply Equation 2 by 3 to make the coefficient of y in both equations equal:

1. \( 3x + 6y = 21 \) (remains the same)
2. \( 3(-5x + 2y) = 3(13) \)
\( -15x + 6y = 39 \) (Equation 3)

Now we have the following system of equations:

1. \( 3x + 6y = 21 \)
2. \( -15x + 6y = 39 \)

**Step 2: Eliminate y.**

Now we will subtract Equation 1 from Equation 3:

\[
(-15x + 6y) - (3x + 6y) = 39 - 21
\]

This simplifies to:

\[
-15x - 3x + 6y - 6y = 18
\]
\[
-18x = 18
\]

**Step 3: Solve for x.**

Divide both sides by -18:

\[
x = -1
\]

**Step 4: Substitute x back to find y.**

Now that we have the value of x, we can substitute \( x = -1 \) back into one of the original equations to find y. We can use Equation 1:

\[
3(-1) + 6y = 21
\]
\[
-3 + 6y = 21
\]
\[
6y = 21 + 3
\]
\[
6y = 24
\]
\[
y = 4
\]

**Step 5: Write the solution.**

The solution to the system of equations is:

\[
(x, y) = (-1, 4)
\]

So the final answer is:

\[
\boxed{(-1, 4)}
\]