Question

GG.1 Is (x, y) a solution to the system of equations?
N46
Is (10,8) a solution to this system of equations?
13x+4y=
–
2
12x–14y=8

Answer 1

To determine if \((10, 8)\) is a solution to the system of equations given:

1. \(13x + 4y = -2\)
2. \(12x - 14y = 8\)

we need to substitute \(x = 10\) and \(y = 8\) into both equations and see if the equations hold true.

**First equation:**
\[
13(10) + 4(8) = -2
\]
Calculating the left side:
\[
130 + 32 = 162
\]
We see that:
\[
162 \neq -2
\]
So, \((10, 8)\) does not satisfy the first equation.

**Second equation:**
\[
12(10) - 14(8) = 8
\]
Calculating the left side:
\[
120 - 112 = 8
\]
We see that:
\[
8 = 8
\]
So, \((10, 8)\) satisfies the second equation.

Since \((10, 8)\) does not satisfy the first equation, we conclude that \((10, 8)\) is not a solution to the system of equations.