Question

Define variables and write a system of equations for the situation. Solve using substitution. A farmer grows only sunflowers and flax on his 240-acre farm. This year he wants to plant 80 more acres of sunflowers than of flax. How many acres of each crop does the farmer need to plant?

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Let xx acres of sunflower and yy acres of flax

x+y=240x+y=240

He want to plant 80 more acres of sunflowers than of flax.

x=y+80x=y+80

Write an equation containing only one variable, and solve it.

x+y=240Start with one equationy+80+y=240 Substitute y+80 for x2y+80=240 Combine like terms2y=160Subtract 80 from both sidesy=80 Divide both sides by 2\begin{align*} x+y&=240 &&\text{{\color{#c34632}Start with one equation}}\\\\ y+80+y&=240 &&\text{{\color{#c34632} Substitute $y+80$ for $x$}}\\\\ 2y+80&=240 &&\text{{\color{#c34632} Combine like terms}}\\\\ 2y&=160 &&\text{{\color{#c34632}Subtract $80$ from both sides}}\\\\ y&=80 &&\text{{\color{#c34632} Divide both sides by 2}}\\\\ \end{align*}

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