Question

Is (
–
1,
–
2) a solution to this system of equations?
7x+8y=13
20x–4y=
–
12

Answer 1

To determine if the point \((-1, -2)\) is a solution to the system of equations given by:

1. \(7x + 8y = 13\)
2. \(20x - 4y = -12\)

we can substitute \(x = -1\) and \(y = -2\) into both equations.

**Step 1: Checking the first equation.**

Substituting into the first equation:
\[
7(-1) + 8(-2) = 13
\]
Calculating the left side:
\[
-7 - 16 = -23
\]
Since \(-23\) does not equal \(13\), \((-1, -2)\) is **not** a solution for the first equation.

**Step 2: Checking the second equation.**

Substituting into the second equation:
\[
20(-1) - 4(-2) = -12
\]
Calculating the left side:
\[
-20 + 8 = -12
\]
Since \(-12\) equals \(-12\), \((-1, -2)\) is a solution for the second equation.

**Conclusion:**

Since the point \((-1, -2)\) does not satisfy the first equation, it is not a solution to the system of equations.