Question

2x+3y=-15
y=-5x+8

Answer 1

To solve the system of equations:

1. \( 2x + 3y = -15 \) (Equation 1)
2. \( y = -5x + 8 \) (Equation 2)

We can substitute Equation 2 into Equation 1.

### Step 1: Substitute \( y \) in Equation 1

Substitute \( y = -5x + 8 \) into the first equation:

\[
2x + 3(-5x + 8) = -15
\]

### Step 2: Simplify the equation

Distributing the \( 3 \):

\[
2x - 15x + 24 = -15
\]

Combine like terms:

\[
-13x + 24 = -15
\]

### Step 3: Solve for \( x \)

Subtract \( 24 \) from both sides:

\[
-13x = -15 - 24
\]
\[
-13x = -39
\]

Now, divide by \( -13 \):

\[
x = 3
\]

### Step 4: Solve for \( y \)

Now substitute \( x = 3 \) back into Equation 2 to find \( y \):

\[
y = -5(3) + 8
\]
\[
y = -15 + 8
\]
\[
y = -7
\]

### Solution

The solution to the system of equations is:

\[
(x, y) = (3, -7)
\]

### Verification

Now, let's verify by substituting \( x = 3 \) and \( y = -7 \) back into both original equations:

1. For Equation 1:
\[
2(3) + 3(-7) = 6 - 21 = -15 \quad \text{(True)}
\]

2. For Equation 2:
\[
y = -5(3) + 8 = -15 + 8 = -7 \quad \text{(True)}
\]

The solution \( (x, y) = (3, -7) \) satisfies both equations.