How to solve the simultaneous equations 3x+2y=7 and 5x+y=14

Firstly we rearrange one of these equations so that we have y on one side of the equation on its own. Let's do this with the second equation.

So from 5x+y=14, we can minus 5x from both sides to get:

y=14-5x

Then we can substitute this expression for y into our first equation that is 3x+2y=7

So we have 3x+2(14-5x)=7

Then we expand the bracket: 

3x+(2)(14)+(2)(-5x)=7

By simplifying this equation we get:

3x+28-10x=7

And simplifying further gives:

7x=21

By dividing both sides by 7, we find that x=3.

We substitute this value for x into either of our original equations to find the value of y.

3(3)+2y=7

So 2y=7-9

And therefore y=-1.

Finally we can check our solutions by substituting x=3 and y=-1 into the other original equation.

Therefore the solutions are x=3 and y=-1.