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# Solve for x:3x+4y=85; 6x+7y=20

The solution of the system of linear equations in two variables can be obtained by various methods.

We will be using the elimination method to solve for x and y respectively.

## Answer: The solution for x and y for x:3x+4y=85; 6x+7y=20 are -515/3 and 150 respectively.

Let's evaluate the equations

**Explanation:**

The given equations are:

3x + 4y = 85 -------------> equation 1

6x + 7y = 20 -------------> equation 2

Multiply the equation (1) by 2 and then subtract it from equation (2)

[** 3x + 4y = 85 ] × 2** ⇒ 6x + 8y = 170

Here we are eliminating x by subtracting the equations

6x + 7y = 20

__(-) 6x + 8y = 170__

-y = -150

⇒ **y =150 **

Let us substitute the value of y in equation (1)

3x + 4y = 85

⇒ 3x + 4(150)= 85

⇒ 3x = 85 - 4(150) = 85 - 600

⇒ 3x = 85 - 600

⇒ 3x = - 515

⇒ **x = -515/3 = -171.67**

### Thus, the solution to the given set of equations are x = -171.67 or -515/3 and y = 150

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