To solve the system of equations:
- \( 2x + 3y = 26 \) (Equation 1)
- \( 5x + 3y = -29 \) (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:
\[ \left(-\frac{55}{3}, \frac{188}{9}\right) \]