Question

our solution.

1. $-2x - 5y = 3$

$3x + 8y = -6$

Explanation:

Step 1: Eliminate one variable (e.g., x)

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x opposites.
First equation: $-2x - 5y = 3$ multiplied by 3: $-6x - 15y = 9$
Second equation: $3x + 8y = -6$ multiplied by 2: $6x + 16y = -12$

Step 2: Add the two new equations

Add $-6x - 15y = 9$ and $6x + 16y = -12$:
$(-6x + 6x) + (-15y + 16y) = 9 + (-12)$
Simplify: $y = -3$

Step 3: Substitute y = -3 into one of the original equations

Use the second original equation: $3x + 8y = -6$
Substitute y = -3: $3x + 8(-3) = -6$
Simplify: $3x - 24 = -6$

Step 4: Solve for x

Add 24 to both sides: $3x = -6 + 24$
$3x = 18$
Divide by 3: $x = 6$

Answer:

The solution to the system of equations is $x = 6$ and $y = -3$.