solve by addition.?

Question

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

can somome please help me with this thank you.

Answer 1

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

To solve this equation by addition, one thing you can do is multiply the second equation by -5. This will give us these two equations.

5x - 4y = -5
-5x + 10y = 35

Now, we add them together. Note that the 5x and -5x will become 0 when added, and thus cancel out. That leaves us with

(-4y) + 10y = -5 + 35
6y = 30
y = 5

Suppose we wanted to eliminate the y variable instead of the x. Then, for

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

We would multiply the second equation by -2. This will give us these two equations:

5x - 4y = -5
-2x + 4y = 14

Adding the two, we have

3x = 9
x = 3

Answer 2

To solve by addition, you need one of the terms to cancel out. So for example, if you mulitplied the 2nd equation by -5, then you'd have -5x. When you added the equations, x would cancel out...

5x - 4y = -5

So mulitply the 2nd equation by -5:
-5x + 10y = 35

Add them
6y = 30

Then divide by 6 on both sides:
y = 5

Now substitute this back into one of the original equations to get x:
x - 2(5) = -7
x -10 = -7
x = 3

So the answer is x = 3, y = 5

Answer 3

set it so that the variable of one set is equal the the negative value of the same variable of the second set. Then just add.

So:
5x-4y=-5
+ [-2(x-2y=-7)]

equals:
5x-4y=-5
+(-2x+4y=14)

equals:
3x=9

x=3

Answer 4

5x-4y= -5
x-2y= -7
5x - 4y = - 5
-2x + 4y = 14
3x = 9
x = 3
3 - 2y = -7
2y = 10
y = 5