Question

Can I get help in solving these problems using the linear system of elimination.

4x - 5y =22
x + 2y = -1


2x - 3y = 16
3x + 4y = 7

Word Problem:
During the summer, you want to earn at least $150 per week. You earn $10 per hour working for a farmer and you earn $5 per hour babysitting for your neighbor. You can work at most 25 hours per week.

I need to write and solve a system of linear inequalities that models the situation. Let x be the number of hours per week working on the farm and let y be the number of hours per week babysitting...

I am not sure but I came up with x+y<=(less than equal) to 25. or is there another solution....Thanks

Answer 1

For your first question, substitute x = -1 -2y into the first equation, leaving you with
-4 -8y -5y = 22, which cqn be rearranged to
-13y = 26
y = -2
2x +6 = 16
2x = 10
x=5

Do your second question the same way.

For your third question, the other inequality you have is
10 x + 5 y >= 150
Solve the "equals" case first.
x + y = 25
10x + 5y = 150
5x + 5y = 125
5x = 25
x = 5
y = 20
If you work more than 5 hours per week at the higher wage, and 20 or less at the lower paying job (but totaling 25 hours) you will earn more than $150 per week. Plot a graph to show the allowed regions of x-y space.