Solve the following linear equation for x and y:3x – 4y = 122x + y = 5

Sure, let's solve the system of equations step by step.

The system of equations is:

1. 3x - 4y = 12
2. 2x + y = 5

Step 1: Solve the second equation for x:

2x = 5 - y x = (5 - y) / 2

Step 2: Substitute x in the first equation:

3((5 - y) / 2) - 4y = 12 (15 - 3y) / 2 - 4y = 12 Multiply through by 2 to get rid of the fraction: 15 - 3y - 8y = 24 Combine like terms: -11y + 15 = 24 Subtract 15 from both sides: -11y = 9 Divide by -11: y = -9/11

Step 3: Substitute y = -9/11 into the second equation:

2x - 9/11 = 5 Multiply through by 11 to get rid of the fraction: 22x - 9 = 55 Add 9 to both sides: 22x = 64 Divide by 22: x = 64/22 = 32/11

So, the solution to the system of equations is x = 32/11 and y = -9/11.