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2x+3y=-15

y=-5x+8

1 answer

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.