Considering the system of these two equations: Equation 1: 3x + 4y = 10 Equation 2: 2x - 6y = 12 What is the solution to this system?

To solve this system of equations, we can use either substitution or elimination method. Here, we will use the elimination method.

Step 1: Multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of x the same in both equations. This gives us:

Equation 1: 6x + 8y = 20 Equation 2: 6x - 18y = 36

Step 2: Subtract Equation 2 from Equation 1 to eliminate x:

(6x + 8y) - (6x - 18y) = 20 - 36 This simplifies to: 26y = -16

Step 3: Solve for y by dividing both sides by 26:

y = -16 / 26 = -8/13

Step 4: Substitute y = -8/13 into Equation 1 (3x + 4y = 10) and solve for x:

3x + 4(-8/13) = 10 3x - 32/13 = 10 3x = 10 + 32/13 3x = 130/13 + 32/13 3x = 162/13 x = 54/13

So, the solution to the system of equations is x = 54/13 and y = -8/13.