Question

solve the linear system using elimination. your answer is an ordered pair (x, y). 2x + y = 10 5x - y = 18 options: (8, 4), (4, 2), (2, 4), (4, 8)

Explanation:

Step1: Add the two equations

We have the system:
\[

$$\begin{cases} 2x + y = 10 \\ 5x - y = 18 \end{cases}$$

\]
Adding the two equations to eliminate \(y\):
\((2x + y)+(5x - y)=10 + 18\)
Simplify the left - hand side: \(2x+y + 5x-y=7x\)
Simplify the right - hand side: \(10 + 18 = 28\)
So we get the equation \(7x=28\)

Step2: Solve for x

From \(7x = 28\), divide both sides by 7:
\(x=\frac{28}{7}=4\)

Step3: Substitute x into the first equation to find y

Substitute \(x = 4\) into \(2x + y=10\):
\(2\times4+y = 10\)
\(8 + y=10\)
Subtract 8 from both sides: \(y=10 - 8=2\)

Answer:

\((4,2)\)