Question

use elimination to solve the system of equations
2x+4y=5
-2x-y=4
the solution is (7/2,-3)
the solution is (-7/2,3)
the solution is (-3,7/2)
the solution is (3,-7/2)

Answer 1

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

1. \( 2x + 4y = 5 \) (Equation 1)
2. \( -2x - y = 4 \) (Equation 2)

To eliminate \(x\), we can add Equation 1 and Equation 2 together. First, we can express Equation 2 by multiplying it by 1 (to keep it unchanged):

\[
-2x - y = 4
\]

Now let's add the two equations:

\[
(2x + 4y) + (-2x - y) = 5 + 4
\]

When we combine like terms, the \(2x\) and \(-2x\) cancel out:

\[
(2x - 2x) + (4y - y) = 9
\]

This simplifies to:

\[
3y = 9
\]

Now, solve for \(y\):

\[
y = \frac{9}{3} = 3
\]

Next, we will substitute \(y = 3\) back into either of the original equations to solve for \(x\). We'll use Equation 1:

\[
2x + 4(3) = 5
\]

This simplifies to:

\[
2x + 12 = 5
\]

Now, isolate \(x\):

\[
2x = 5 - 12
\]

\[
2x = -7
\]

\[
x = \frac{-7}{2}
\]

Thus, the solution to the system of equations is:

\[
\left(-\frac{7}{2}, 3\right)
\]

So, the correct answer among the options provided is:

**The solution is \((-7/2, 3)\)**.