Question 580848: Please show me step by step how to do this
solve the systems of equations 2x - y = 6, x + 5 y = -19
My work thus far--I have done this, but not sure if it is right?
2x-2x-y=6-2x
y=6-2x
y-intercept is (0,6)
slope is -2
Now this is the part that does not come out? I dont know what i am doing wrong
SOMEONE PLEASE HELP ME!
x + 5 y = -19
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the system of equations to solve:
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2x - y = 6 and
x + 5y = -19
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At this stage of your studies in math, there are a couple of ways that you can solve this system. You can use substitution or you can use variable elimination. Whatever you do, don't try to do too much in your head, because if you make a mistake you won't be able to find what you did wrong.
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So let's try substitution first. Pick one of the equations and solve it for one variable in terms of the other. In this case, it might be easier to select the second equation because we can easily solve it for x in terms of y. In the second equation we can can get rid of the 5y term by subtracting 5y from both sides. This makes the 5y on the left side go away and the right side becomes as shown below:
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x = -19 -5y
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Now with that result from the second equation, we can go to the first equation and substitute -19 - 5y for x. When we replace x in the first equation with (-19 - 5y) the first equation becomes:
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2(-19 - 5y) - y = 6
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Do the distributed multiplication by multiplying 2 times each of the terms in the parentheses and you have:
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-38 - 10y - y = 6
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Get rid of the -38 on the left side by adding +38 to both sides. On the left side adding +38 to -38 results in zero, so the -38 disappears. On the right side adding +38 results in the sum of 38 and 6 which is +44. Therefore, the equation is:
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-10y - y = 44
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Combining the two terms on the left side results in:
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-11y = 44
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And by dividing both sides by -11 you arrive at:
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y = -4
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Finally you can solve for x by going to either of the two equations and substituting -4 for y. Let's go to the second equation and replace y by -4 to make it become:
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x + 5(-4) = -19
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Multiplying the 5 times -4 results in -20 and the equation is then:
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x - 20 = -19
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Get rid of the -20 on the left side by adding +20 to both sides and you get:
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x = -19 + 20 = +1
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The two answers for the unknowns in this system of equations are x = +1 and y = -4.
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Let's check this solution by working the problem in a different way to see if we get the same answer. The second way will involve variable elimination. Start with the two equations:
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2x - y = 6 and
x + 5y = -19
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We're going to subtract (or add) in vertical columns and eliminate one of the variables in doing so. Let's think about eliminating y. We can make y in the first equation equal the y term in the second equation. All we have to do is multiply the first equation (all terms on both sides) by 5. When we do that the first equation becomes:
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10x - 5y = 30
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Let's put the second equation right below it so this pair of equations is:
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10x - 5y = 30 and
x + 5y = -19
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Adding vertically we get: the 10 + x = 11x, the -5y and the +5y cancel each other out, and the 30 and -19 add to give +11. So after adding we are left with 11x on the left side and 11 on the right side as follows:
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11x = 11
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Solve for x by dividing both sides by 11 to get:
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x = 1
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Then you can return to either of the original equations and substitute +1 for x to solve for y. Let's go to the second equation and substitute +1 for x. When we do that the second equation becomes:
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1 + 5y = -19
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Get rid of the 1 by subtracting 1 from both sides to get:
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5y = -20
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and solve for y by dividing both sides by 5. The answer becomes:
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y = -4
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So using variable elimination results in x = 1 and y = -4. These are the same results as we got working the problem using substitution, so our answer checks.
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Hope this helps you to see how you can use these two methods to solve a system of linear equations. All it takes is a little understanding and lots of practice in using these methods.
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