The original equation over here was 3x minus 2y is equal to 3. We're doing the same thing to both sides of it. Let's say we have 5x plus 7y is equal to 15. Which equation is correctly rewritten to solve for x 3 0. You divide 7 by 7, you get 1. On the left hand side of the equation, the q numerator will cancel the q denominator, leaving us with only x). We're going to have to massage the equations a little bit in order to prepare them for elimination. Check the full answer on App Gauthmath.
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Combine and simplify the denominator. It should be equal to 15. So let's say that we have an equation, 5x minus 10y is equal to 15. Now, we can start with this top equation and add the same thing to both sides, where that same thing is negative 25, which is also equal to this expression. In some cases, we need to slightly manipulate a system of equations before we can solve it using the elimination method. Let's substitute into the top equation. Which equation is correctly rewritten to solve for x? -qx+p=r - Brainly.com. First we need to subtract p from both-side of the equation. Provide step-by-step explanations. The constants are the numbers alone with no variables. Remember, we're not fundamentally changing the equation. 64y is equal to 105 minus 25 is equal to 80. Now, is there anything that I can multiply this green equation by so that this negative 2y term becomes a term that will cancel out with the negative 10y? How can you determine which number to multiply by?
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So the left-hand side of the equation becomes negative 5 times 3x is negative 15x. Or we get that-- let me scroll down a little bit-- 7x is equal to 35/4. So this top equation, when you multiply it by 7, it becomes-- let me scroll up a little bit-- we multiply it by 7, it becomes 35x plus 49y is equal to-- let's see, this is 70 plus 35 is equal to 105. And what do you get?
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Ask a live tutor for help now. The left side does not satisfy the equation because the fraction cannot be divided by zero. So let's pick a variable to eliminate. Still have questions? At2:20where did the -5 come from? So 5x minus 15y-- we have this little negative sign there, we don't want to lose that-- that's negative 10x.
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So that becomes 10/8, and then you can divide this by 2, and you get 5/4. And you are correct. To solve for x, we make x subject of the formula. So if you looked at it as a graph, it'd be 5/4 comma 5/4. And we have 7-- let me do another color-- 7x minus 3y is equal to 5. Which is equal to 60/4, which is indeed equal to 15. Systems of equations with elimination (and manipulation) (video. These aren't in any way kind of have the same coefficient or the negative of their coefficient. Let's do another one of these where we have to multiply, and to massage the equations, and then we can eliminate one of the variables. If you multiply 3x + 2y = 18 by -2 (I chose -2 so when you add the equations together, variables cancel out), you get -6x - 4y = -36. These lines are parallel; they cannot intersect. And I can multiply this bottom equation by negative 5. You can say let's eliminate the y's first. Qx = r - p. We want to make the left hand side of the equation positive, so we simply multiply through by a negative sign (-).
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But even a more fun thing to do is I can try to get both of them to be their least common multiple. And that's going to be equal to 5, is the same thing as 20/4. He is adding, not subtracting. Next, use the negative value of the to find the second solution. This would be 7x minus 3 times 4-- Oh, sorry, that was right. So I'll just rewrite this 5x minus 10y here. Which equation is correctly rewritten to solve for x seeks. And you could really pick which term you want to cancel out. Change both equations into slope-intercept form and graph to visualize. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur. Combining like terms, we end up with.
The same thing as dividing by 7. Divide each term in by. Negative 10y plus 10y, that's 0y. The our equation becomes.
Let's multiply both sides by 1/7.