Answer
$$x=22$$ $$y=-6$$
Work Step by Step
Let $x$ be the larger number and $y$ be the smaller number.
Equation 1: $x\:+\:y = 16$
Equation 2: $3x-y=72$
We can solve for the numbers using the addition method.
Adding equations & 2:
$$x\:+\:y = 16$$ $$+$$ $$3x-y=72$$ $$=$$ $$4x=88$$
Divide both sides by $4$:
$$\frac{4x}{4}=\frac{88}{4}$$ $$x=22$$
Substitute this value of $x$ to equation 1:
$$x\:+\:y = 16$$ $$22+y=16$$
Subtract $22$ from both sides:
$$22-22+y=16-22$$ $$y=-6$$
Use equation 2 to check:
$$3x-y=72$$ $$3(22)-(-6)=72$$ $$66+6=72$$ $$72=72$$
