Question

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

2x+3y=11
y=3x

Answer 1

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

1. \( 2x + 3y = 11 \) (Equation 1)
2. \( y = 3x \) (Equation 2)

### Step 1: Substitute Equation 2 into Equation 1

Since Equation 2 expresses \( y \) in terms of \( x \), we can substitute \( y \) with \( 3x \) in Equation 1.

\[
2x + 3(3x) = 11
\]

### Step 2: Simplify the equation

Now, simplify the equation:

\[
2x + 9x = 11
\]

Combine like terms:

\[
11x = 11
\]

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

Now, divide both sides by 11:

\[
x = 1
\]

### Step 4: Substitute \( x \) back to find \( y \)

Now that we have \( x \), we will substitute \( x = 1 \) back into Equation 2 to find \( y \):

\[
y = 3(1) = 3
\]

### Step 5: Write the solution

Thus, the solution to the system of equations is:

\[
(x, y) = (1, 3)
\]

### Step 6: Verify the solution

We can substitute these values back into the original equations to verify that both equations are satisfied:

1. Check Equation 1:

\[
2(1) + 3(3) = 2 + 9 = 11 \quad \text{(True)}
\]

2. Check Equation 2:

\[
y = 3x \implies 3 = 3(1) \quad \text{(True)}
\]

Both equations are satisfied, so our solution \( (1, 3) \) is correct.

### Final Answer:
The solution to the system of equations is:

\[
(x, y) = (1, 3)
\]