Posted by **JAY10** on Thursday, March 12, 2009 at 1:29am.

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

- math/algebra -
**drwls**, Thursday, March 12, 2009 at 6:15am
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.

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