Solve the system by addition.?

Question

Solve the system by addition.
5x – 4y = –5
x – 2y = –7

Answer 1

(1) Multiply the second equation by -2 (so that the resulting coefficient of y, +4, will cancel -4 in the first equation). Then add vertically.

5x - 4y = -5
x - 2y = -7

5x - 4y = -5
-2x + 4y = 14
============
3x + 0y = 9

3x = 9 reduces to
x = 3

(2) Multiply the second equation by -5 (so that the resulting coefficient of x, -5, will cancel +5 in the first equation). Then add vertically.

5x - 4y = -5
x - 2y = -7

5x - 4y = -5
-5x + 10y = 35
============
0x + 6y = 30

6y = 30 reduces to
y = 5.


The solution is x=3, y=5. Use either (or both) original equation to check:

5x - 4y = -5
5*3 - 4*5 =? -5
15 - 20 =? -5
-5 = -5

Answer 2

5x – 4y = –5
x – 2y = –7

You need to first decide which term you want to eliminate first. EIther x, or y.

So, im going to eliminate the x term first. Now I need to make
the second equation have -5 on the x term. so I am going to multiply the 2nd equation by a scalar of 5.

1) 5x – 4y = –5
2) (x – 2y = –7) * -5 --> -5x + 10y = -35

Second equation now looks like : -5x + 10y = -35

1) 5x – 4y = –5
2) -5x + 10y = -35

Add down.. x term eliminate 5x - 5x = 0

6y = 40

y = 40/6


Now we must eliminate the y term..
1) 5x – 4y = –5
2) x – 2y = –7

NOTE how that im using the original equations again..

I need to make the 2nd equation y term to have a positive 4. So i am going to multiply the 2nd equation by a scalar of -2


1) 5x – 4y = –5
2) (x – 2y = –7) * -2 --> -2x +4y = 14

2nd equation now becomes: -2x +4y = 14


5x – 4y = –5
-2x +4y = 14

Adding down..


3x = 9

x = 9/3 -> 3

so your answers are x = 3, and y = 40/6

Answer 3

x=4 and y=2

Answer 4

5x-4y=-5 eq1
x-2y=-7 eq2

multiply the second equation by -5
-5x+10y=35 eq2a

add eq2a and eq1
5x-4y=-5
-5x+10y=35

yields 6y=30
therefore y=5

solve for x

x-2y=-7
x-2(5)=-7
x=-7+10
x=.3

Answer 5

x-y=2

Answer 6

Before you add them, multiply the second row by -2, making it

-2x + 4y = 14

Then add like terms, the y terms go away, leaving 3x = 9 from which you can get what x is. Then plug this in to either equation (or both to be sure) and get y.

Answer 7

5x - 4y = - 5
- 2x + 4y = 14----ADD
3x = 9
x = 3

3 - 2y = - 7
2y = 10
y = 5

x = 3 , y = 5

Answer 8

Are you just looking for an answer? I will help.

Set on of your equations equal to one of the variables.

Another example:

6x - 3y = 72

x-3y = 6

In the second equation x - 3y = 6 it becomes x = 3y + 6

Substitute 3y + 6 into your first equation in place of the x since you say that x = 3y + 6

you get 6(3y +6) -3y = 1; 18y + 36 = 72; 18y = 36; y = 2