How can i solve the following simultaneous equations? 5x + y = 4 and 3x + 2y = 5?

The general approach to solving simultaneous equations is to replace the ‘y’s in one equation with ‘x’s, or the ‘x’s with ‘y’s.

In this case, we can first take the equation 5x + y = 4 and rearrange it to get the ‘y’ on one side.



Rearranged to:



Using this new rearranged equation we can replace the ‘y’s in the other equation.

Where we have ‘y’ in 3x + 2y = 5, we can replace it with 4 - 5x.



We can then start to simplify our new equation.



Rearranging until we reach x = 3/7. We can then replace this value of ‘x’ into either of the equations.

For example, we can replace our value of ‘x’ in 5x + y = 4.



Finally, we can expand and rearrange the equation to find ‘y’.



Therefore, the value of ‘x’ is 3/7 and the value for ‘y’ is 13/7.