How do I solve this pair of simultaneous equations: 3x+y=7 and 3x-y=5?

Step 1: Eliminate the ‘y’ component from the equations by adding the equations together. This gives the new equation ‘6x=12’

Step 2: Find the value of x by dividing both sides of the equation by 6. This gives us the value of x=2.

Step 3: Use this value of x to find the value of y, by substituting x=2 into one of the two original equations. For example, using the first equation: 6+y=7. By subtracting 6 from both sides of the equation, we find that y=1.

Step 4 (optional but recommended): To check that these values of x and y are correct, substitute both these found values into the original equation that you haven’t already used. Using the second equation, we can verify that 3x-y=5 is correct when x=2 and y=1. We can therefore have full confidence that we have the correct answer!