Question

Consider the system of equations.
y = −2x + 4 y = −
1
3
x − 1
The solution is (3, –2).
Verify the solution. Which true statement appears in your check?
4 = 4
–2 = –2
–1 = –1
–3 = –3

Answer 1

To verify the solution \((3, -2)\) for the system of equations, we can substitute \(x = 3\) and \(y = -2\) into both equations.

For the first equation:
\[
y = -2x + 4
\]
Substituting \(x = 3\) and \(y = -2\):
\[
-2 = -2(3) + 4
\]
\[
-2 = -6 + 4
\]
\[
-2 = -2 \quad \text{(true)}
\]

Now, for the second equation:
\[
y = -\frac{1}{3}x - 1
\]
Substituting \(x = 3\) and \(y = -2\):
\[
-2 = -\frac{1}{3}(3) - 1
\]
\[
-2 = -1 - 1
\]
\[
-2 = -2 \quad \text{(true)}
\]

Since both equations hold true, the solution \((3, -2)\) is indeed correct.

Now, evaluating the true statements provided:
- \(4 = 4\) (true)
- \(-2 = -2\) (true)
- \(-1 = -1\) (true)
- \(-3 = -3\) (true)

However, since the verification of the solution directly provided \(-2 = -2\) for the second equation, it specifically shows the agreement with the found value \(y\) in the context of the system of equations. Therefore, we can conclude that the statement \(-2 = -2\) appears in our check.