# How do I solve simultaneous equations? Such as 2x + 4y = 8, 3x + 2y = 8.

There are two easy ways to solve simultaneous equations. Substitution and elimination. In order to work with substitution we must rearrange one equation to be equal to either x or y. In this case, 2x+4y=8, can be rearranged and simplified to get x=4-2y. We then take this new equation and substitute it into the other equation we had from the start. So, 3x+2y=8 becomes 3(4-2y)+2y=8. This simplifies to 12-4y=8, and by solving this new equation for y we get that y=1. We can then substitute this value for y into either of our first equations to find x: 2x+4y=8 becomes 2x+4=8, which when solved for x gives us that x=2.The other method, elimination, involves adding/subtracting one whole equation to/from the other. In order to do this we need to have either the same amount of x's or the same amount of y's in both equations. This can be achieved by multiplying both equations by separate numbers (one of these numbers can be 1, in this example it is.) In this case, I am going to make sure that we have the same number of y's in both equations. Since we have four in one equation and two in the other I am going to multiply the entire equation containing 2y by two, as this gives me 4y. So, 3x+2y=8 then becomes 6x+4y=16. Now we subtract one equation from the other to get rid of all of the y's. (6x-2x)+(4y-4y)=(16-8) simplifies down to 4x=8, which simplified again gives us that x=2. Now that we have one variable's value we jut substitute it into any equation like before. 3x+2y=8 would become 6+2y=8, which simplifies down to y=1.

Answered by Cameron T. Maths tutor

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