Answer
The larger number is $8$ while the smaller number is $4$.
Work Step by Step
Let $x$ be the larger number and $y$ be the smaller number.
Equation 1: $x+y=12$
Equation 2: $3y+x=20$
Multiply equation 1 by $-1$:
$$[x+y=12]\cdot-1$$ $$-x-y=-12$$
Add this equation to equation 2:
$$-x-y=-12$$ $$+$$ $$3y+x=20$$ $$=$$ $$2y=8$$
Divide both sides by $2$:
$$\frac{2y}{2}=\frac{8}{2}$$ $$y=4$$
Substitute this value of $y$ to equation 1:
$$x+y=12$$ $$x+4=12$$
Subtract $4$ from both sides:
$$x+4-4=12-4$$ $$x=8$$
Use equation $2$ to check:
$$3y+x=20$$ $$3(4)+8=20$$ $$12+8=20$$ $$20=20$$
