Answer
Sarah and Owen Hebert purchased $17$ pieces of 13¢ stamps and $9$ pieces of 22¢ stamps.
Work Step by Step
Let $x$ be the number of 13¢ stamps and $y$ be the number of 22¢ stamps.
Equation 1: $x+y=26$
Equation 2: $0.13x+0.22y=4.19$
Multiply equation 1 by $-0.22$.
$$[x+y=26]\cdot-0.22$$ $$-0.22x-0.22y=-5.72$$
Add this equation to equation 2:
$$-0.22x-0.22y=-5.72$$ $$+$$ $$0.13x+0.22y=4.19$$ $$=$$ $$-0.09x=-1.53$$
Divide both sides by $-0.09$:
$$\frac{-0.09x}{-0.09}=\frac{-1.53}{-0.09}$$ $$x=17$$
Substitute this value of $x$ to equation 1:
$$x+y=26$$ $$17+y=26$$
Subtract $17$ from both sides:
$$17-17+y=26-17$$ $$y=9$$
Use equation 2 to check:
$$0.13(17)+0.22(9)=4.19$$ $$2.21+1.98=4.19$$ $$4.19=4.19$$
