# Solve the following system of equations 3x - 4y = 25 -2x + y = -10

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We have to solve the system of equations

- 3x - 4y = 25

- -2x + y = -10

3x - 4y = 25

=> 3x = 25 + 4y

=> x = ( 25 + 4y)/3

substitute in -2x + y = -10

=> -2 ( ( 25 + 4y)/3) + y = -10

=> ( 25 + 4y)/3 - y/2 = 5

=> 2( 25 + 4y) - 3y = 30

=> 50 + 8y - 3y = 30

=> 5y = -20

=> y = -20/ 5

=> y = -4

x = ( 25 + 4y)/3

=> (25 - 16) / 3

=> 9/3

=> 3

**Therefore x = 3 and y = -4**

3x -4y = 25.........(1)

-2x + y = -10...........(2)

We will use the elimination method to solve.

Multiply (2) by 4.

==> -8x + 4y = -40

Now we will add to (1).

==> -5x = -15

Now we will divide by -5.

==> x = 3

Now, from (2) we will rewrite:

y= -10 + 2x

==> y= -10+2*3 = -10+ 6 = -4

==> y= -4

**Then, the solution to the system is : x= 3 and y= -4 or the pair (3,-4).**

3x - 4y = 25

-2x + y = -10

First, multiply everything on the second equation by 4.

By multiplying, your equation should look like

**3x - 4y = 25**

**-8x + 4y = -40 **now, add -4y with 4y ( so add 3x with -8x and 25 with -40 also )

**-5x = -15 **now divide both sides by -5

By dividing, your equation should look like

**x = 3 **which is your answer for " x "

Now plug 3 into one of the equation

**-2 ( 3 ) + 4y = -10 **multiply -2 with 3

By multiplying, your equation should look like

**-6 + 4y = -10 **now add 6 on both sides

By adding, your equation should look like

**4y = -16 **now divide both sides by 4

By dividing your equation should look like

**y = -4 ** which is your answer for " y "

So your answer is **x = 3 ; y = -4**

-2x+y=-10

-2x+y+2x=-10+2x

y=-10+2x

3x-4(-10+2x)=25

3x+40-8x=25

-5x+40=25

-5x+40-40=25-40

-5x=-15

-5x/-5=-15/-5

x=3

3(3)-4y=25

9-4y=25

9-4y-9=25-9

-4y=16

-4y/-4=16/-4

y=-4

We'll multiply the 2nd equation by 4 and we'll solve the system using elimination:

3x - 4y - 8x + 4y = 25 - 40

-5x = -15

x = 3

We'll substitute x into the 2nd equation:

-2*3 + y = -10

We'll move the numbers alone to the right side:

y = 6 - 10

y = -4

**The solution of the system is represented by the pair: (3 ; -4).**