# What is the solution for x: 3x + 19y = 6, 4x + 21y = 4

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### 2 Answers

We have to solve the following equations for x:

3x + 19y = 6 ...(1)

4x + 21y = 4 ...(2)

As we only have to find x, we can substitute for y in (1) using (2)

From (2) we get

21y = 4 - 4x

=> y = (4 - 4x)/21

Substitute in (1)

3x + 19(4 - 4x)/21 = 6

=> 63x + 76 - 76x = 126

=> -13x = 50

=> x = -50/13

**The required value of x = -50/13**

I reccomend using elimination to solve this problem:

>3x + 19y = 6

4x + 21y = 4

>4*(3x + 19y = 6)

-3*(4x + 21y = 4)

>12x + 76y = 24

-12x - 63y = -12

>Cancel x and we have:

76y = 24

-63y = -12

>Now you just need to add both y's together, and since it's 76 + (-63), we have:

13y = 12

>Divide by 13 on both side to solve for y, we have:

y = 12/13

>Now that we know y, substitute it back into on of the original equations to solve for x:

3x + 19(12/13) = 6

3x + 228/13 = 6

3x = -150/13

x = -50/13.

Hope I helped......