Name: matthew

simultanious equations question

what is
4x + y = 4
2x - 3y = 5

what is x and y

looks impossible...

Hi Matthew,

You have two equations in two unknowns, x and y, and the standard way to approach such problems is to "eliminate one of the unknowns" and change the problem to one involving a single equation in one unknown. I can see two ways to approach this particular problem, eliminate x or eliminate y.

Eliminate x

The first step is to manipulate the equations so that the coefficients of x in the two equations are the same. You can do this by muliplying both sides of the second equation by 2. This gives

4x + y = 4
4x - 6y = 10

Subtracting the second equation from the first results in

(4x + y) - (4x - 6y) = 4 - 10 or

7y = -6
Hence y = -6/7 and substitution into either of the two equations you started with will yield x.

Eliminate y

If you multiply both sides of the first equation by 3 you can eliminate y. Thus

12x + 3y = 12
2x - 3y = 5

and adding the two equations yields

(12x + 3y) + (2x - 3y) = 12 + 5

14x = 17
Hence x = 17/14 and substitution will yield y.

I hope this helps,
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