To determine which equation [tex]\( (-4, -3) \)[/tex] does not satisfy, we need to substitute the coordinates [tex]\( x = -4 \)[/tex] and [tex]\( y = -3 \)[/tex] into each given equation and verify the results.
1. Equation 1: [tex]\( 5x + 2y = -26 \)[/tex]
Substitute [tex]\( x = -4 \)[/tex] and [tex]\( y = -3 \)[/tex]:
[tex]\[
5(-4) + 2(-3) = -20 - 6 = -26
\][/tex]
The left side equals the right side ([tex]\(-26\)[/tex]), so [tex]\( (-4, -3) \)[/tex] is a solution to the first equation.
2. Equation 2: [tex]\( 2y - 3x = 6 \)[/tex]
Substitute [tex]\( x = -4 \)[/tex] and [tex]\( y = -3 \)[/tex]:
[tex]\[
2(-3) - 3(-4) = -6 + 12 = 6
\][/tex]
The left side equals the right side ([tex]\(6\)[/tex]), so [tex]\( (-4, -3) \)[/tex] is a solution to the second equation.
3. Equation 3: [tex]\( -3x = 4y \)[/tex]
Substitute [tex]\( x = -4 \)[/tex] and [tex]\( y = -3 \)[/tex]:
[tex]\[
-3(-4) = 4(-3)
\][/tex]
Simplify both sides:
[tex]\[
12 \neq -12
\][/tex]
The left side does not equal the right side, so [tex]\( (-4, -3) \)[/tex] is not a solution to the third equation.
4. Equation 4: [tex]\( y = 1 + x \)[/tex]
Substitute [tex]\( x = -4 \)[/tex] and [tex]\( y = -3 \)[/tex]:
[tex]\[
-3 = 1 + (-4) = -3
\][/tex]
The left side equals the right side ([tex]\(-3\)[/tex]), so [tex]\( (-4, -3) \)[/tex] is a solution to the fourth equation.
After checking all four equations, we conclude that [tex]\( (-4, -3) \)[/tex] is not a solution for the equation:
[tex]\[ -3x = 4y \][/tex]
Thus, the correct equation for which [tex]\( (-4, -3) \)[/tex] is not a solution is the third one:
[tex]\[
-3x = 4y
\][/tex]
