Solve this using the Addition Method: 2x+3y=13 and then under that 4x+5y=22?

Answer 1

2x+3y=13
4x+5y=22
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Multiply the first equation by -2:
-4x-6y=-26
4x+5y=22
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-y=-4
y=4

4x+5(4)=22
4x+20=22
4x=2
x=1/2

The solution set is (1/2,4)

Check:
2(1/2)+3(4)=13
1+12=13
13=13

4(1/2)+5(4)=22
2+20=22
22=22

Answer 2

First, eliminate y by multiplying the first equation by –5 and the second equation by 3:
[2x + 3y = 13] -5
[4x + 5y = 22] 3

-10x – 15y = -65
12x + 15y = 66

2x + 0 = 1
x = ½

Next, we eliminate x by multiplying the first equation by –2:

[2x + 3y = 13] -2
4x + 5y = 22

-4x – 6y = -26
4x + 5y = 22

0 + -y = -4
y = 4

x = ½
y = 4

2x + 3y = 13
2( ½ ) + 3 (4) = 13
1 + 12 = 13
13 = 13

4x + 5y = 22
4( ½ ) + 5 (4) = 22
2 + 20 = 22
22 = 22

Answer 3

Elimination by Addition Method

2x + 3y = 13- - - - --Equation 1
4x + 5y = 22- - - - - Equation 2
- - - - - - - - -

Multiply equation 1 by - 2

2x + 3y = 13

-2(2x) + (- 2)(3Y) = - 2(13)

- 4x + (- 6y) = - 26

-4x - 6y = - 26

- - - - - - - - - - - -

Elimination of x

-4x - 6y = - 26
4x + 5y = 22

- y = - 4

-1(- y) = -1(-4)

y = 4

The answer is y = 4

Insert the y value into the equation 1

- - - - - - - - - - - - - - - - - - - - - - - -

2x + 3y = 13

2x + 3(4) = 13

2x + 12 = 13

2x + 12 - 12 = 13 - 12

2x = 1

2x / 2 = 1 / 2

x = 1 / 2

x = 0.5

The answer is x = 0.5

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - -

Check for equation 1

2x + 3y = 13

2().5) + 3(4) = 13

1 + 12 = 13

13 = 13

- - - - - - - -

Check for equation 2

4x + 5y = 22

4(0.5) + 5(4) = 22

2 + 20 = 22

22 = 22

- - - - - - - - -

The solution set is { 0.5, 4 }

- - - - - -s-

Answer 4

2x + 3y = 13
4x + 5y = 22

if you multiply the entire top equation by -2 it will make the x-terms opposites. I'll explain why this is important later. We get--

-4x + -6y = -26
4x + 5y = 22

Now add the 2 equations together

-4x + -6y = -26
4x + 5y = 22
__________________

0x + -1y = -4 or -y = -4 or y = 4

the reason we multiplied the top equation by -2 was so the x-terms would add to 0 and make the x's "disappear" from the set of equations leaving us with only y-terms. You sometimes have to be a little sneaky to figure out how to do this part of the solution but with practice you can usually get to be pretty sneaky!! But wait!!! We aren't done!!!!!!!!!

Now you can pick either of the original equations and substitute 4 in place of "y" and find out what "x" is. I pick the first equation.

2x + 3 ( 4 ) = 13
2x + 12 = 13
2x = 13 - 12
2x = 1
x = 1/2.

You try putting y = 4 into the second equation. You should get the same thing.

I hope this haelp you a little!!!

Answer 5

2x+3y=13 multiply by -2
-4x-6y=-26
4x+5y=22 add
-y=-4 divide both sides bt -1
y=4
substitute into
4x+5y=22
4x+5*4=22
4x+20=22 subtract 20 from each side
4x=2 divide by 4
x=1/2
(1/2, 4) check by substituting into
2x+3y=13
2(1/2)+3*4=13
1+12=13
13=13

Answer 6

2x+3y=13....1]
4x+5y=22.....2]
double eqn. 1
4x+6y=26......3]
3] -2] we have
y=4
substitute in 1]
2x+12=13
2x=1
x=1/2

Answer 7

My keyboard is a bit troublesome, so I am unable to use signs and so spelling them out. Hope its clear.
Its a simultaneous equation sum
Multiply the first equation by 2, you get
4x plus 6y equal to 26
Now, subtract the second equation from the first you get,
y equal to 4
substituting y equal to 4 in any equation you get x equal to half
so u have x equal to half and y equal to 4
hope you are satisfied
Ask some tough questions, not such easy ones

Answer 8

2x+3y=13 *-2
-4x-6y=-26
4x+5y=22
adding
-y=-4
y=4
subs
2x+12=13
2x=1
x=1/2

Answer 9

Add them: 6x + 8y = 35. Re-arrange them: 8y = -6x + 35. Divide by 8: y = -3/4 x + 4 3/8. I think this is a line with a slope of -3/4 and a y intercept of 4 3/8.

(Now: I'm writing about 5 minutes after initially submitting my answer. "yupchagee" looks a heck of a lot "righter" than I!) R.S.

Answer 10

no longer in basic terms the mattress, the closet too. ;-; If I dropped one in each and every of my crammed animals off of the mattress whilst i grew to become into attempting to sleep, and the room grew to become into dark, i could permit it stay there with the aid of fact i concept something could grab my arm from decrease than the mattress as i attempted to %. it up. :3 i do no longer have confidence that stuff anymore however. I nonetheless get spooked through the closet if I watch an extremely frightening horror action picture however. >->