Solve these simultaneous equations: 2x + y = 7, and 3x - y = 8. Do so by 1) Eliminating an Unknown and 2) Substitution.

1. The number 'in front of' an unknown is called the Coefficient. When eliminating an unknown, look to see whether the coefficients of x are the same in both equations, or if the coefficients of y are the same. In this case, the y coefficients are both 1, and so we can 'get rid of' y from our equations.

Adding the equations together we get; 2x + 3x + y - y = 7 + 8  --->  5x + 0 = 15  --->   x = 3           The y's cancel out.

Then subsitute x = 3 into either equation, we'll use the first;   2(3) + y = 7  --->  6 + y = 7  --->  y = 1 

2. By substitution. Rearrange one of the equations to get x = ... or y = ... . If we rearrange the first equation we get  y = 7 - 2x.

Now we can substitute  y = 7 - 2x into the second equation;  3x - (7 - 2x) = 8. Use brackets here so that we don't get confused with signs.

Expand this out;  3x - 7 + 2x = 8  --->  5x = 15  --->  x = 3

Then substitute x = 3 into our 'y' equation;   y = 7 - 2(3)  --->  y = 7 - 6   --->   y = 1 

We get x = 3 and y = 1 with both methods.