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

Question

i dont know how to do this

please explain

Thanks

Answer 1

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

 

 

Answer 2

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

Answer 3

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!

Answer 4

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!