Word problems with systems of equations | Algebra 2

Two unknowns, two facts

Many real problems involve two unknown quantities and give you two separate facts about them. Each fact becomes an equation, and together they form a system.

Useful translations:

Words	Algebra
the sum of $$x$$ and $$y$$ is $$64$$	$$x + y = 64$$
$$x$$ is $$18$$ more than $$y$$	$$x = y + 18$$
$$y$$ is $$5$$ more than twice $$x$$	$$y = 2x + 5$$
$$x$$ pounds at $$6$$ dollars per pound	cost $$6x$$
$3\%$ interest on $$x$$ dollars	$$0.03x$$

Worked problems

Practice

Quick check

Which equation says " $$y$$ is 5 more than twice $$x$$ "?

Quick check

Ten coins, all nickels and dimes, are worth 70 cents. How many nickels are there?

Words	Algebra
the sum of $\(x\)$ and $\(y\)$ is $\(64\)$	$\(x + y = 64\)$
$\(x\)$ is $\(18\)$ more than $\(y\)$	$\(x = y + 18\)$
$\(y\)$ is $\(5\)$ more than twice $\(x\)$	$\(y = 2x + 5\)$
$\(x\)$ pounds at $\(6\)$ dollars per pound	cost $\(6x\)$
$3\%$ interest on $\(x\)$ dollars	$\(0.03x\)$