Solve the simultaneous equation: 2x + y = 7 and 3x - y = 8

The aim of this maths question is to find the two unknowns, x and y, by using simultaneous equations. Simultaneous equations can be solved by either using the elimination method or the substitution method. Today we are going to use the substitution method. Step 1: Write both equations out on top of each other and label them (1) and (2) respectively, like so: 2x + y = 7 (1) 3x - y = 8 (2) Step 2: Now we want to either get one equation in the form of either y = ax + b, or x = ay + b by rearranging it. By doing this, it makes it easier to substitute one equation into the other. Lets look at equation (1) for example: 2x + y = 7 now to rearrange it in to the form we mentioned above, minus 2x from both sides to get: y = 7 - 2x (1) Step 3: now we can substitute equation (1) in its new form into equation (2), like so: 3x - (7 - 2x) = 8 Step 4: It is important to remember when we times out the bracket, a minus times a minus equals a plus, a plus times a plus equals a plus, and a minus times a plus equals a minus. So the new equation becomes: 3x - 7 + 2x = 8 Step 5: add both the x terms together: 5x - 7 = 8 Step 6: rearrange by adding a 7 to both sides: 5x = 15 Step 7: divide both sides by 5, to get our x term: x=3 Step 8: now you have the x term, we need to find the y term. we do this by substituting our x term back into one of our first equations. For example lets use equation (1): 2(3) + y = 7 6 + y = 7 Step 9: now rearrange to find your y term by subtracting 6 from both sides to get: y = 1 So your answer is x = 3 and y = 1