Lloyd,
I think you are to solve the system of equations
2x + 5y = 3
x + 3y = 7
That is you want to find two numbers x and y that satisfy both equations. The first thing I am going to do is multiply both sides of the second equation by 2. (You will see why in a moment.) This gives me
2x + 5y = 3
2x + 6y = 14
The left side of the first equation is equal to the right side of the first equation and the left side of the second equation is equal to the right side of the second equation. Thus the sum of the left side of the first equation and the left side of the second equation is equal to the sum of the right side of the first equation and the right side of the second equation. that is
(2x + 5y) + (2x + 6y) = (3 ) + (14), or
11 y =  11 and thus
y = 1.
I hope now why I multiplied the second equation by 2. It was to make the x terms cancel above.
Now that you know the value of y you can substitute that value into either equation you started with and solve for x.
Once you have x and y you should substitute the values into both equations you started with to verify that your answer is correct.
Penny
