Answer
Infinite solutions
The solutions are the points on the line $y = \frac{2}{3}x + \frac{13}{3}$.
Work Step by Step
Given:
$4x - 6y = -26$
$-2x + 3y = 13$
Multiply both sides of the second equation, $-2x + 3y = 13$, by $2$.
Gives: $-4x + 6y = 26$
Add the equations, $4x - 6y = -26$ and $-4x + 6y = 26$:
$4x - 6y + (-4x + 6y) = -26 + (26)
\\4x - 4x - 6y + 6y = -26 + 26$
Combine like terms:
$0 = 0$
This statement is true.
This implies that
Therefore, there are infinite solutions to this problem.
Solve for $y$ to find the formula for solutions.
Using the first equation: $4x - 6y = -26$
Divide both sides by $2$: $2x - 3y = -13$
Add $3y$ to both sides: $2x = -13 + 3y$
Add $13$ to both sides: $2x + 13 = 3y$
Divide both sides by $3$: $\frac{2}{3}x + \frac{13}{3} = y$
Therefore, the solutions to the given system of linear equations are all the points on the line $y = \frac{2}{3}x + \frac{13}{3}$.