Questions: For which of the following equations is (-2,-5) a solution? 4y=8-6x -2x-5y=0 4y-2x=2 6x-3y=3

Transcript text: For which of the following equations is $(-2,-5)$ a solution? $4 y=8-6 x$ $-2 x-5 y=0$ $4 y-2 x=2$ $6 x-3 y=3$

Solution

Solution Steps

To determine which of the given equations has $(-2, -5)$ as a solution, we need to substitute $x = -2$ and $y = -5$ into each equation and check if the equation holds true. If the left-hand side equals the right-hand side after substitution, then $(-2, -5)$ is a solution for that equation.

Step 1: Substitute the Point into Each Equation

To determine which equation has $(-2, -5)$ as a solution, substitute $x = -2$ and $y = -5$ into each equation:

$4y = 8 - 6x$ \[ 4(-5) = 8 - 6(-2) \implies -20 = 8 + 12 \implies -20 = 20 \] This is false.
$-2x - 5y = 0$ \[ -2(-2) - 5(-5) = 0 \implies 4 + 25 = 0 \implies 29 = 0 \] This is false.
$4y - 2x = 2$ \[ 4(-5) - 2(-2) = 2 \implies -20 + 4 = 2 \implies -16 = 2 \] This is false.
$6x - 3y = 3$ \[ 6(-2) - 3(-5) = 3 \implies -12 + 15 = 3 \implies 3 = 3 \] This is true.