If 2x + y = 13 and 3x - y = 12, what are the values for x and y?

To solve these simulataneous equations we need to use substitution:If 2x + y = 13 then y = 13 - 2xTherefore 3x - y = 12 can be rewritten as 3x - (13 - 2x) = 12We can expand these brackets and solve for x:3x - 13 + 2x = 12-> 5x = 25--> x = 5Now we have the value of x, we can subsitute this into either of the initial equations to find the value of y:2(5) + y = 13--> 10 + y = 13--> y = 3OR:3(5) - y = 12--> 15 - y = 12--> y = 3You can then check your values are correct by subsituting them into either of the equations:2(5) + (3) = 1310 + 3 = 13 --> it works!