What is the solution of the system?

2x+3y=26 5x+3y=-29

1 answer

To solve the system of equations:

  1. \( 2x + 3y = 26 \) (Equation 1)
  2. \( 5x + 3y = -29 \) (Equation 2)

We can use the elimination method.

First, we'll subtract Equation 1 from Equation 2 to eliminate \(3y\).

Subtract Equation 1 from Equation 2:

\[ (5x + 3y) - (2x + 3y) = -29 - 26 \]

This simplifies to:

\[ 5x - 2x = -29 - 26 \]

\[ 3x = -55 \]

Now, solve for \(x\):

\[ x = -\frac{55}{3} \]

Next, we can substitute \(x\) back into one of the original equations to find \(y\). We'll use Equation 1:

\[ 2(-\frac{55}{3}) + 3y = 26 \]

This simplifies to:

\[ -\frac{110}{3} + 3y = 26 \]

To eliminate the fraction, multiply the entire equation by 3:

\[ -110 + 9y = 78 \]

Now, solve for \(y\):

\[ 9y = 78 + 110 \]

\[ 9y = 188 \]

\[ y = \frac{188}{9} \]

So the solution to the system of equations is:

\[ x = -\frac{55}{3}, \quad y = \frac{188}{9} \]

In ordered pair form, the solution is:

\[ \left(-\frac{55}{3}, \frac{188}{9}\right) \]