Question

Solve the system below using ELIMINATION. Show step-by-step work to earn credit. Use the Format Editor x−−√ to type math or use the Image icon to upload a photo of your work.

3x−2y=0
2x+y=7

Answer 1

To solve the system of equations using elimination, we have the following two equations:

1. \( 3x - 2y = 0 \) (Equation 1)
2. \( 2x + y = 7 \) (Equation 2)

### Step 1: Prepare the equations for elimination

We can choose to eliminate \( y \) by manipulating the second equation. To do this effectively, we can multiply the second equation by \( 2 \) so that the coefficients of \( y \) will match in magnitude, thus allowing us to eliminate \( y \):

\[
2(2x + y) = 2(7)
\]

This gives us:

\[
4x + 2y = 14 \quad \text{(Equation 3)}
\]

Now we have the following system:

1. \( 3x - 2y = 0 \) (Equation 1)
2. \( 4x + 2y = 14 \) (Equation 3)

### Step 2: Add the equations to eliminate \( y \)

Now, we will add Equation 1 and Equation 3 together:

\[
(3x - 2y) + (4x + 2y) = 0 + 14
\]

Combining like terms gives:

\[
3x + 4x - 2y + 2y = 14
\]

This simplifies to:

\[
7x = 14
\]

### Step 3: Solve for \( x \)

Now, divide both sides by \( 7 \):

\[
x = 2
\]

### Step 4: Substitute \( x \) back into one of the original equations

Now that we have \( x = 2 \), we can substitute this value into one of the original equations to find \( y \). We will use Equation 2:

\[
2(2) + y = 7
\]

This gives:

\[
4 + y = 7
\]

### Step 5: Solve for \( y \)

Now, subtract \( 4 \) from both sides:

\[
y = 7 - 4
\]

So we have:

\[
y = 3
\]

### Step 6: Write the solution

Thus, the solution to the system of equations is:

\[
\boxed{(2, 3)}
\]

### Summary of the Solution Steps:
1. Use elimination by adjusting one equation to match coefficients.
2. Add the equations to eliminate one variable.
3. Solve for the remaining variable.
4. Substitute back to solve for the other variable.
5. Present the solution.