To solve this system, you could do the following steps:

Question

3x+4y=48

6x+2y=60

(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1. Choose the best method to solve by looking at the way the equations are set up for you: Response area

2. Using the best method, how could you get the x variables to cancel out? Response area

3. After you complete step 2, what would your top equation be? Response area

4. Line them up and add the equations together to get this equation. Response area

5. Solve for y. Response area

6. Solve for x. Response area

there is no option for y = 15.6 its y = 18 y = 6 x = 8 x = 6 y = -12 x = -3 there's also no 10y = 156

Answer 1

Let's solve the system of equations step by step using elimination or substitution.

The given equations are:

1. \( 3x + 4y = 48 \) (Equation 1)
2. \( 6x + 2y = 60 \) (Equation 2)

Step 1: Choose the best method to solve.

Response area: Elimination method

Step 2: How to get the x variables to cancel out?

To eliminate \(x\), we can multiply Equation 1 by 2, making the coefficients of \(x\) the same in both equations.

Response area: Multiply the first equation (Equation 1) by 2.

Step 3: What would your top equation be after step 2?

After multiplying Equation 1 by 2: \[ 2(3x + 4y) = 2(48) \implies 6x + 8y = 96 \] So, the new top equation is: Response area: \(6x + 8y = 96\)

Step 4: Line them up and add the equations together.

Now we have:

1. \(6x + 8y = 96\) (Modified Equation 1)
2. \(6x + 2y = 60\) (Equation 2)

Let's subtract Equation 2 from the modified Equation 1 to eliminate \(x\): \[ (6x + 8y) - (6x + 2y) = 96 - 60 \] This simplifies to: \[ 6y = 36 \]

Response area: \(6y = 36\)

Step 5: Solve for y.

To find \(y\), divide both sides by 6: \[ y = \frac{36}{6} = 6 \]

Response area: \(y = 6\)

Step 6: Solve for x.

Now that we have \(y\), we can substitute it back into one of the original equations to solve for \(x\). Let's use Equation 1: \[ 3x + 4(6) = 48 \] This simplifies to: \[ 3x + 24 = 48 \implies 3x = 48 - 24 \implies 3x = 24 \] Dividing by 3 gives us: \[ x = \frac{24}{3} = 8 \]

Response area: \(x = 8\)

Final solution:

• \(x = 8\)
• \(y = 6\)

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