Question

Solve the system of linear equations 30x+50y=100 3x-15y=30

Answer 1

Answer:

(x, y) = (5, -1)

Step-by-step explanation:

First of all, look at the equations. The first would be in standard form if it were divided by 10. (Here, we're calling this process "normalization," for lack of a better term) Doing that gives coefficients of 3, 5, 10. The second would be in standard form if divided by 3. Doing that gives coefficients 1, -5, 10.

At this point, you observe a couple of opportunities to use elimination to solve these equations. Since the x-coefficients match after the first normalization, we can subtract one equation from the other at that point. (That is what we did below.)

Since the y-coefficients are opposites after the second normalization, we could simply add the two equations to eliminate y. Either way rapidly gets you to an answer.

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Choose an approach and work the problem

Divide the first equation by 10 and subtract the second equation.

... (3x +5y) -(3x -15y) = (10) -(30)

... 20y = -20

... y = -1

From either equation we can find x. Using the second one ...

... 3x -15(-1) = 30

... 3x = 15 . . . . . . subtract 15

... x = 5 . . . . . . . . divide by 3