#18 - #22 Solve the following systems of equations: 10x - 2y = -13 -2x + 3y = 13

Question

#18 - #22

Solve the following systems of equations: 10x - 2y = -13 -2x + 3y = 13 x + 6y + 3z = 4 2x + y + 2x = 3 3x - 2y + z = 0 x - 2y = -1 -3x + 6y = 5 2x + 2y + z = 6 4x - 3y + z = -8 -2x - 6z = 5 A company produces Italian sausages and bratwursts at plants in Green Bay and Sheboygan, WI. The Green Bay plant can produce 800 Italian sausages per hour and 800 bratwursts per hour. The Sheboygan plant can produce 500 Italian sausages per hour and 1000 bratwursts per hour. How many hours should each plant operate to fill an order of exactly 62, 250 Italian sausages and 76.500 bratwursts?

Explanation / Answer

Question 18:

The system of linear equations here is:

10x - 2y = -13....................................(1)

-2x + 3y = 13

Multiplying the second equation by 5 we get:

-10x + 15y = 65

Adding the above equation to the equation (1) we get:

15y - 2y = 65 - 13

13y = 52

y = 52/ 13 = 4

Put this in equation (1) to get:

10x - 2*4 = -13

10x - 8 = -13

10x = -5

x = -0.5

Therefore the final values here are x = -0.5 and y = 4

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