Question

4x + 5y = 50 7x + 12y = 94 Solve by add/ elimination

Answer 1

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

1. \( 4x + 5y = 50 \) (Equation 1)
2. \( 7x + 12y = 94 \) (Equation 2)

To eliminate one of the variables, we can manipulate these equations. We'll aim to eliminate \(y\). To do this, we first need the coefficients of \(y\) in both equations to be the same.

We can achieve this by multiplying Equation 1 by 12 and Equation 2 by 5:

1. Multiply Equation 1 by 12:
\[
12(4x + 5y) = 12(50)
\]
\[
48x + 60y = 600 \quad (Equation 3)
\]

2. Multiply Equation 2 by 5:
\[
5(7x + 12y) = 5(94)
\]
\[
35x + 60y = 470 \quad (Equation 4)
\]

Now we have the following system of equations:
- Equation 3: \( 48x + 60y = 600 \)
- Equation 4: \( 35x + 60y = 470 \)

Next, we subtract Equation 4 from Equation 3 to eliminate \(y\):

\[
(48x + 60y) - (35x + 60y) = 600 - 470
\]
\[
48x - 35x = 130
\]
\[
13x = 130
\]

Now, we solve for \(x\):

\[
x = \frac{130}{13} = 10
\]

Now that we have \(x\), we substitute \(x = 10\) back into one of the original equations to find \(y\). We'll use Equation 1:

\[
4(10) + 5y = 50
\]
\[
40 + 5y = 50
\]
\[
5y = 50 - 40
\]
\[
5y = 10
\]
\[
y = \frac{10}{5} = 2
\]

Thus, the solution to the system of equations is:

\[
\boxed{(10, 2)}
\]