Answer
Exactly one solution.
Work Step by Step
Step 1
Solve one of the equations for one of the variables.
Select the second equation, solve for $x$.
$ 3x+6y=22 \qquad$ ... add $-6y$
$ 3x=-6y+22\qquad$ ... divide with $3$
$x=-2y+\displaystyle \frac{22}{3}$
Step 2
Substitute $-2y+\displaystyle \frac{22}{3}$ for $x$ in the other equation and solve for $y$
$1.5x+2y=11$
$\displaystyle \frac{3}{2}(-2y+\frac{22}{3})+2y=11$
$-3y+11+2y=11\qquad$ ... add $-11$
$-y=0$
The variable has not vanished, so there is exactly one solution.
x is obtained by substituting $0 $ for $y$ in $x=-2y+\displaystyle \frac{22}{3}$
$x=\displaystyle \frac{22}{3}$
Solution: $(\displaystyle \frac{22}{3},0)$
