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math/algebra

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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 -

    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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