# Solve the following equations: 7x-4y=-10 and 4y=x-2.

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We have to solve the simultaneous equations

7x-4y=-10 ...(1)

4y=x-2...(2)

add (2) and (1)

=> 7x - 4y + 4y = -10 + x - 2

=> 7x = -12 + x

=> 6x = -12

=> x = -2

Substitute this in (2)

4y=x-2

=> 4y = -2 - 2

=> 4y = -4

=> y = -1

**Therefore we get x = -2 and y = -1.**

7x-4y= -10. Or -4y = -7x-10...(2)....(1)

4y =x-2, or 4y = x-2 ...(2).

(1)+(2) eliminates y: -4y+4y = -7x-10+x-2.

=> 0 = -7x+x-10-2.

=> 0 = -6x-12.

=> 6x= -12. Or x = 12/-6 = -2.

Put x= -2 in 4y= x-2 . 4y = -2-2 = -4, or y = -4/4 = -1.

Therefore x= -2 and y = -1.

So x= 1 and y = -2.

To perform elimination method we need to have 2 like variables that have opposite sign.

To see more clear how to act, we'll need to write both equations in the same manner: we'll isolate to the left side the variables and we'll move the numbers alone to the right side.

The first equation needs no changes but the second will turn into:

4y - x = -2

We'll re-arrange the terms:

-x + 4y = -2

Now, the system will become:

7x - 4y = -10 (1)

-x + 4y = -2 (2)

We can remark that we can eliminate the variable y, since in both equations there are terms 4y and -4y.

We'll add (1)+(2) to eliminate y;

7x - 4y - x + 4y = -10 - 2

We'll combine and eliminate like terms:

6x = -12

We'll divide by 6:

x = -2

Now, we'll substitute x in the second equation:

-(-2) + 4y = -2

2 + 4y = -2

We'll subtract 2 to isolate y to the left side:

4y = -4

y = -1

**The solution of the system solved using elimination method is: (-2 ; -1).**