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how to solve each system by elimination 5x+y=9 and 10x-7y=-18

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4 Answers

Hi Angelica;
5x+y=9 and 10x-7y=-18
The coefficients of x are 5 and 10.  To apply the practice of elimination, we want only one coefficient.
Let's take the first equation...
5x+y=9
Let's multiply both sides by 2...
2(5x+y)=(9)(2)
10x+2y=18
Let's subtract this from the second equation...
10x-7y=-18
-(10x+2y=18)
10x-10x=0
-7y-2y=-9y
-18-18=-36
0-9y=-36
The x is eliminated.
-9y=-36
Let's divide both sides by -9...
(-9y)/-9=-36/-9
A negative number divided by a negative number has a positive result...
y=4
Let's plug this into either equation to establish the value of x.  I randomly select the second...
10x-7y=-18
10x-[(7)(4)]=-18
10x-28=-18
Let's add 28 to both sides...
28+10x-28=-18+28
10x=10
Let's divide both sides by 10...
(10x)/10=10/10
x=1
Let's plug both values into the first equation to verify results...
5x+y=9
[(5)(1)]+4=9
5+4=9
9=9
 
 
First, align each equation: 
5x  +   y = 9
10x - 7y = -18
Second, you must eliminate the x's or the y's.  Let's choose the y's.  Therefore, multiply the top equation by 7 (both sides of the equal sign)
7 * (5x + y) = 9 * 7
35x + 7y = 63
10x - 7y  = -18  Now, add the two equations.  This gives a result of
45x = 45  Divide both sides by 45 and x = 1.
Substitute x = 1 into either original equation  5 (1) + y = 9;  5 + y = 9.  Subtract 5 from both sides of equal sign.  y = 4.
Answer  x = 1 and y = 4
To answer this by elimination do the following:
 
5x+y=9
10x-7y=-18
 
Multiply top equation by -2
 
-2(5x+y)=9(-2)
10x-7y=-18
 
Now multiply out the -2 in the first equation:
 
-10x-2y=-18
10x-7y=-18
 
Now vertically add the comonents:
-9y=-36  <---- (-10x + 10x = 0, -2y + -7y = -9y, and -18 + -18 = -36)
 
Divide each side by -9
 
-9y/-9 = -36/-9
 
y=4
 
Not just substitute 4 back into an equation and solve for x:
 
5(x) + 4 = 9
 
5(x) = 5
 
x = 1
 
Now double check your work (use the opposite equation to make sure)
 
10(1)-7(4)=-18
10-28=-18
-18=-18
 
Viola! All done. I hope you enjoyed this step-by-step answer!
5x+y=9 .... multiply both sides by 2 ... 10x+2y=18
10x-7y = -18
 
subtract the second equation from the first, giving 9y = 36 [2y-(-7y)= 9y; 18- (-18) = 36]
y=4
substitute y = 4 into either equation, solve for x
I'll use the second ... 10x-(7)(4) = -18 ... 10x-28 = -18 ... 10x = 10 (adding 28 to both sides) ... x= 1
 
Check for correctness using the first equation 5*1+4 = 9?  yes, it does!

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