Question

solve the following system of equations using the elimination method.
$2x + y = 3.5$, $-x + 2y = 2.5$
(1 point)
(\boxed{\quad},\boxed{\quad})

Explanation:

Step1: Multiply the second equation by 2

To eliminate \(x\), we multiply the second equation \(-x + 2y = 2.5\) by 2. This gives us \(-2x + 4y = 5\).

Step2: Add the first equation to the new second equation

The first equation is \(2x + y = 3.5\). Adding it to \(-2x + 4y = 5\) (from Step 1), we get \((2x - 2x)+(y + 4y)=3.5 + 5\), which simplifies to \(5y = 8.5\).

Step3: Solve for \(y\)

Divide both sides of \(5y = 8.5\) by 5: \(y=\frac{8.5}{5}=1.7\).

Step4: Substitute \(y\) into the first equation to solve for \(x\)

Substitute \(y = 1.7\) into \(2x + y = 3.5\), we get \(2x+1.7 = 3.5\). Subtract 1.7 from both sides: \(2x=3.5 - 1.7 = 1.8\). Then divide by 2: \(x=\frac{1.8}{2}=0.9\).

Answer:

\((0.9, 1.7)\)