# What is the solution for 3x + 4y = 10 and 2x + 9y = 20

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3x+4y = 10 .........(1)

2x+9y = 20 ..........(2)

We will use elemination method to solve:

First we will multiply eq.(1) with -2 and eq.(2) with 3:

==> -2(3x+4y = 10) ==> -6x - 8y = -20

==> 3(2x+9y= 20) ==> 6x + 27y = 60

Now add both equations:

==> 19y = 40

**==> y= 40/19**

Now 2x + 9y = 20

==> x= (20-9y)/2

= (20-9*40/19)/2

= (380-360)/2*19

= 10/19

**==> x= 10/19**

We have the equations

3x + 4y = 10… (1)

2x + 9y = 20… (2)

Now we have to use (1) and (2) to find the value of x and y.

First perform the operation 2*(1) – 3*(2)

=> 2*(3x + 4y) - 3*(2x + 9y) = 2*10 – 3*20

=> 6x + 8y – 6x – 27y = 20 – 60 = -40

=> -19y = -40

=> y = 40/19

Next, substitute y = 40/19 in (1)

=> 3x + 4*(40/19) = 10

=> 3x = 10 -4*(40/19)

=> 3x = (190-160)/19

=> x = 10/19

**Therefore the value of x that satisfies the equations is 10/19 and the value of y is 40/19.**

3x + 4y = 10

2x + 9y = 20

First, multiply everything in the top equation by 2 and everything in the second equation by 3

By multiplying, your equation should look like

**6x + 8y = 20 **

**6x + 27y = 60 **now subtract 6x with 6x (which means subtract 8y with 27y and 20 with 60)

By subtracting, your equation should look like

**-19y = -40 **divide both sides by -19

By dividing, your equation should look like

**y = 49/19 **which is your answer for " y "

now plug 40/19 into one of the equation

By doing that, your equation should look like

**3x + 4 ( 40/19 ) = 10** multiply 40/19 with 4

By multiplying, your equation should look like

**3x + 160/19 = 10 **subtract both sides by 160/19

By subtracting, your equation should look like

**3x = 30/19 **now divide both sides by 3

By dividing, your equation should look like

**x = 10/19 **which is your answer for " x "

So your answer is **x = 10/19 ; y = 40/19**

To find the solution for the equations, 3x+4y = 10 ...(1) and 2x+9y = 20 ...(2).

From the 2nd eqution we get 2x=20-9y. Or x = (20-9y)/2. We substitute x = (20-9y)/2 in the first equation:

3(20-9y)/2 + 4y = 10.

Multiply by 2:

3(20-9y) +8y = 20.

60 -27y +8y = 20.

-19y = 20-60 = -40.

y = -40/-19 .

y = 40/19.

Substitute y = 40/19 in equatin 2x+9y = 20:

2x +9(40/19) = 20.

2x = 20-360/19.

2x = (380-360)/19 = 20/19

x = 20/(2*19) = 10/19.

Therefore x= 10/19 and y = 40 /19.