Answer
Infinitely many
Work Step by Step
Step 1
Solve one of the equations for one of the variables.
$ 6y+5x=8\qquad$ ... subtract 5x
$ 6y=8-5x\qquad$ ... divide with 6
$y=\displaystyle \frac{4}{3}-\frac{5}{6}x$
Step 2
Substitute $\displaystyle \frac{4}{3}-\frac{5}{6}x$ for $y$ in the other equation, and solve for $x$
$2.5x+3(\displaystyle \frac{4}{3}-\frac{5}{6}x)=4$
$2.5x+4-\displaystyle \frac{5}{2}x=4\qquad $... since $\displaystyle \frac{5}{2}=2.5$, we have
$4=4$
The variable has vanished, and the resulting equation is a true one, so
the system has infinitely many solutions.
