last year lien earned 1,700 more than her husband. Together they earned 42,100. howm much did each of them earn?

Let x = the salary of the husband.

So Lien earned x+1700.
Lien's salary + her husband's = 42100
x + 1700 + x = 42100
2x + 1700 = 42100
2x = 40400
x = 20200
Lien's husband earned $20200, and Lien earned 1700 + 20200 = $23900.

To determine how much each of them earned, let's set up equations based on the given information:

Let's assume the husband's earnings are represented by H, and Lien's earnings are represented by L.

1) "Last year Lien earned $1,700 more than her husband."
This can be expressed as: L = H + $1,700

2) "Together they earned $42,100."
This can be expressed as: L + H = $42,100

Now, we have a system of equations:
Equation 1: L = H + $1,700
Equation 2: L + H = $42,100

We can solve this system of equations to find the values of L (Lien's earnings) and H (husband's earnings).

Substitute Equation 1 into Equation 2:
(H + $1,700) + H = $42,100
2H + $1,700 = $42,100

Subtract $1,700 from both sides:
2H = $42,100 - $1,700
2H = $40,400

Divide both sides by 2:
H = $40,400 / 2
H = $20,200

Now we know that the husband's earnings, H, are $20,200.

Substitute this value back into Equation 1 to find Lien's earnings, L:
L = $20,200 + $1,700
L = $21,900

Therefore, Lien earned $21,900 and her husband earned $20,200.