Question

Solve the system using elimination 2x + 4y = 10 3x + 5y = 11 (1 point) Responses (4,-3) (4,-3) (3,1) (3,1) (-3,4) (-3,4) no solution

Answer 1

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

1) \( 2x + 4y = 10 \)
2) \( 3x + 5y = 11 \)

First, let's multiply the first equation by a factor that will allow us to easily eliminate \(x\) or \(y\). We'll use the first equation and multiply it by 3:

\[
3(2x + 4y) = 3(10) \\
6x + 12y = 30 \quad \text{(Equation 3)}
\]

Next, we'll multiply the second equation by 2:

\[
2(3x + 5y) = 2(11) \\
6x + 10y = 22 \quad \text{(Equation 4)}
\]

Now we have two new equations:

3) \( 6x + 12y = 30 \)
4) \( 6x + 10y = 22 \)

Next, we'll subtract Equation 4 from Equation 3 to eliminate \(6x\):

\[
(6x + 12y) - (6x + 10y) = 30 - 22 \\
12y - 10y = 8 \\
2y = 8 \\
y = 4
\]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to solve for \(x\). We'll use the first equation:

\[
2x + 4(4) = 10 \\
2x + 16 = 10 \\
2x = 10 - 16 \\
2x = -6 \\
x = -3
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-3, 4)
\]

Therefore, the answer is \((-3, 4)\).