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Question 627686: Solve 5x – 6y = –38
3x + 4y = 0
Please show work
Answer by 56592526(1)   (Show Source):
You can put this solution on YOUR website! There are a few ways to approach this. Ultimately, you need to find a point (x,y) where the 2 lines would intersect, if graphed. So, the solution is the one unique point that these lines share. Since they are in standard form, it makes sense to solve using "elimination" as the technique. This requires you to make either the x's or the y's have opposite coefficients. Since the y's are already opposite signs, we'll eliminate the y's. In order to eliminate them, the coefficients will be changed to -12y on the top equation and +12y on the bottom equation. The way to do that is to multiply each of the equations, the top equation by 2 and the bottom equation by 3:
2[5x - 6y = -38] becomes: 10x -12y = -76
3[3x + 4y = 0] becomes: 9x +12y = 0
perform three "mini" problems: 19x = -76 (10x+9x=19x,12y+12y=0,-76+0=-76)
solve for x by dividing both sides by 19: 1x = -76/19 or x = -4
now, sub that value back into either equation to find the corresponding y
9(-4) + 12y = 0
-36 + 12y = 0
12y = 36 so y = 3
your answer is (-4, 3). CHECK IT by subbing those back into each equation to make sure they make true statements:
5(-4) - 6(3) = -38? -20 - 18 = -38 YES!
3(-4) + 4(3) = 0? -12 + 12 = 0 YES!
You know you have the correct point of intersection, which is the solution.
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