## Algebra: A Combined Approach (4th Edition)

$$x=22$$ $$y=-6$$
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: $$3x-y=72$$ $$3(22)-(-6)=72$$ $$66+6=72$$ $$72=72$$