Х-3у=4 -х+у=-8

To solve this system of equations, we can use the method of elimination.

Step 1: Multiply each term in the second equation by (-1) to make the co-efficient of x positive: -х + у = -8 ... multiply by (-1) х - у = 8

Step 2: Add the two equations together to eliminate the x term: (х - 3у) + (х - у) = 4 + 8 2х - 4у = 12

Step 3: Solve this new equation for one of the variables. Let's solve for x: 2х - 4у = 12 2х = 12 + 4у х = 6 + 2у

Step 4: Substitute this expression for x into one of the original equations. Let's use the first equation: х - 3у = 4 (6 + 2у) - 3у = 4 6 + 2у - 3у = 4 -у + 6 = 4 -у = 4 - 6 -у = -2 у = 2

Step 5: Substitute the value of у into the expression for x: х = 6 + 2у х = 6 + 2(2) х = 6 + 4 х = 10

Therefore, the solution to the system of equations is x = 10 and y = 2.