i am stuck on a question like this one plese help me solve it step by step so i can figure the other out?

Question

solve by addition

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

Answer 1

First we have to multiply of the equation to make either the x or y value the same in both equations.

Let's multiply 2 to both sides of the equation
x - 2y = -7

2(x - 2y) = 2(-7)
2x - 4y = -14

So now we stack up the equations

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

We can subtract downwards and

5x - 2x = 3x
(-4y)-(-4y) = 0
-5 - (-14) = 9

so 3x + 0 = 9
3x = 9
x = 3

We plug x = 3 into one of the 2 equations to get the y value

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

So, x = 3 and y = 5 is the answer

Answer 2

Write down the equations
(EQ 1) 5x - 4y = -5
(EQ2) x - 2y = -7
Multiply the second equation by 5
(EQ 3) 5x - 10y = -35

Subtract EQ 3 from EQ 1
(EQ 4) 0x +6y = +30

Divide by 6
(EQ 5) y = 30/6 = 5

Plug this value of y back into EQ 2
(EQ 6) x - 2(5) = -7
(EQ 7) x - 10 = -7
(EQ 8) x = -7 + 10 = 3

So the answer is:
x = 3
y = 5

Check:
5x - 4y =? -5
5(3) - 4(5) =? -5
15 - 20 =? =5
-5 =? -5
Yes, so the answer checks.

Answer 3

Hello

So we have
5x-4y=-5
x-2y=-7

So lets subtract these equations (thus adding negatives).

This is also called the Elmination method. We need to eliminate a variable. Lets multiple the 2nd equation by -5.

So we have
5x-4y=-5
-5(x-2y=-7) = -5x+10y=35

Now lets add these equations:
5x-4y=-5
-5x+10y=35

6y = 30
Thus y=5 and plug this into any equation to get x = 3.

Hope this helps

Answer 4

5x-4y=-5..........(1)
x-2y=-7..........(2)
By eliminating one of the unknown variables easily the value of the other can be calculated. To do this one of the variables should be made equal.(No matter what sign it is). Let us take "y". By multiplying all the terms in equation (2) by "2" the term of "y" will become 4y. Quantitatively, this is equal to the "y" term in equation (1). To eliminate, addition or subtraction can be done. In the case of "x" if you multiply the equation (2) by "5" the "x" term will become equal.

(2) * 5 = 5x - 10y = -35..........(3)
(3) - (1) = ...... -6y = -30
. . . . . . . . . . . . . . y = -30/-6 = 5
Now, substitute the value of "y" in any one of the given equations. Let us take eqn (2)
x - 2 * 5 = -7
x - 10 . . = -7
x . . . ... . = -7 +10 = 3
Hence, the value of x=3 and the value of y = 5.........Ans.
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Answer 5

5x-4y=-5 <-- Eq 1
x-2y=-7 <-- Eq 2
-2x +4y =14 <-- Eq 3 = Eq 2 * -2
3x = 9 <-- Eq3 + Eq 1
x = 3
3-2y = -7
-2y = -10
y = -5