Solve the system: 2x + y = 6,   -2x + 3y = 5

Step 1: Write down the system of equations

2x + y = 6 -2x + 3y = 5

Step 2: Add the two equations together

2x + y + (-2x + 3y) = 6 + 5 0x + 4y = 11 4y = 11

Step 3: Solve for y

Divide both sides by 4 y = 11/4 y = 2.75

Step 4: Substitute y = 2.75 into the first equation

2x + 2.75 = 6 2x = 6 - 2.75 2x = 3.25

Step 5: Solve for x

Divide both sides by 2 x = 3.25/2 x = 1.625

So, the solution to the system of equations is x = 1.625 and y = 2.75.