Linear equations in two variables

Question

A married couple had a combined annual income of $63,000. The wife made $7,000 more than her husband. What was each of their incomes?

Answer 1

Married couple need 2 separate variables. Wife = w; Husband = h

w + h = $63,000 (their combined annual income)

Wife made $7,000 more than her husband. More than is associated with addition (+)

w = $7000 + h

Now, you can substitute w to solve for h

w + h = $63,000

$7,000 + h + h = $63,000

$7,000 + 2h = $63,000

subtract (-) $7,000 from both sides

2h = $63,000 - $7,000

2h = $56,000

h = $28,000

now plug in h to the original equation to find w

w + $28,000 = $63,000

subtract $28,000 from both sides

w = $35,000

w + h = $63,000

$35,000 + $28,000 = $63,000

make sure to check your work