Question

Which ordered pair is the solution to the system below?

x+2y=4
2x−y=−2(1 point)
Responses

(0,2)
(0,2) - correct

(2,0)
(2,0) - no response given
Question 2
Show the step-by-step work that proves your answer above. Use the Formula Editor x−−√ to enter math work or use the Image icon to upload a photo of your work.(2 points)

Answer 1

To find the solution to the system of equations:

1. **Write down the equations**:
\[
x + 2y = 4 \quad \text{(Equation 1)}
\]
\[
2x - y = -2 \quad \text{(Equation 2)}
\]

2. **Substitute one variable**:
To eliminate one of the variables, we can solve one equation for one variable in terms of the other. Let's solve Equation 1 for \(x\):
\[
x = 4 - 2y
\]

3. **Substitute into the second equation**:
Now, substitute \(x\) from Equation 1 into Equation 2:
\[
2(4 - 2y) - y = -2
\]
Simplifying this:
\[
8 - 4y - y = -2
\]
\[
8 - 5y = -2
\]
Now, solve for \(y\):
\[
-5y = -2 - 8
\]
\[
-5y = -10
\]
\[
y = 2
\]

4. **Substitute \(y\) back into Equation for \(x\)**:
Now that we have \(y\), substitute it back into \(x = 4 - 2y\):
\[
x = 4 - 2(2)
\]
\[
x = 4 - 4
\]
\[
x = 0
\]

5. **Final solution**:
So the solution to the system of equations is the ordered pair:
\[
(x, y) = (0, 2)
\]

Thus, the ordered pair that is the solution to the system is \((0, 2)\).