Expert: Josh - 5/12/2004

Question
My 9th grader needs help with a problem, can you help?

Solve the system.
2x + 5y = 7
4x - 3y = -25

multiple choice answers are
a. -4, 3
b.  1, -1
c. -7, -1
d. -9, -5
e. not here

Thank you.

Answer
Solving simultaneous equations
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2x + 5y = 7    ...[Equation 1]
4x - 3y = -25  ...[Equation 2]

You have two unknowns (x and y) and two independent equations. The idea is to solve for these unknowns (x or y) one at a time and eliminate the other variables while you are at it.

Let's say, we work out what "y" represents first.
We have 2x+5y=7, multiplying this equation by 2 does not change the validity of this equation.
That is, equation 1 is the same as
4x+10y=14.    ...call this [Equation 1A]

Now, subtracting [Equation 2] from [Equation 1A], we get
(4x-4x) + 10y-(-3y) = 14-(-25)
13y=39
dividing both sides by 13 gives y=3 as the solution.

The remaining task is to work out what "x" is.
Substituting y=3 into either equation, say the first one,
2x+5(3)=7
2x=7-15
2x=-8
x=-4.

So, the solutions are x=-4,y=3.