How do you solve 2x plus y equals 2 and x plus y equals 1 with steps?

Answer 1

These are known as simultaneous equations. To solve them you must change (if needed) one or both of the equations so that they can be combined in a way which eliminates one of the variables. See below:

1. 2x + y = 2

2. x + y = 1

There is little work to be done for this question. In both equations we have the variable y (and it is a single instance of positive y in each). Therefore, if we subtract one of equations from the other then y will disappear as y - y = 0.

So, subtracting 2. from 1.

[to do this just subtract each term in 2. from the corresponding term in 1. i.e. 2x - x, y - y and 2 -1]

gives:

3. x = 1 (often it is not quite as straightforward as getting the solution in one step, but we shan't complain!)

Now that we have a value for x, we just need to substitute this value back into one of the original equations and we will be able to solve for y.

So substituting x = 1 into 1. gives:

(2*1) + y = 2

2 + y = 2

y = 2 - 2

y = 0.

Therefore the solution is x = 1 and y = 0.