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Kimberly
New Member

USA
1 Posts

Posted - 09/24/2007 :  16:46:55  Show Profile
Please solve step by step with substitution"
7x-4y=2

5x+3Y=-22
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Mrspi
Advanced Member

USA
998 Posts

Posted - 09/24/2007 :  18:18:33  Show Profile
quote:
Originally posted by Kimberly

Please solve step by step with substitution"
7x-4y=2

5x+3Y=-22



Personally, I would NOT use substitution to solve this system. Why? Because you can't solve one of the equations for one of the variables without introducing fractions. This would be much easier to solve using the "addition-elimination" method.

But...since you asked....

Let's take the first equation, and solve it for y:
7x - 4y = 2
Add -7x to both sides:
-4y = -7x + 2
Divide both sides by -4:
y = (7/4)x - (1/2)

Now, substitute (7/4 x - 1/2) for y in the second equation:

5x + 3y = -22

5x + 3(7/4 x - 1/2) = -22
5x + (21/4)x - (3/2) = -22

Ok....let's get rid of the fractions. Multiply both sides of the equation by the common denominator for the fractions, which is 4:

4*5x + 4*(21/4)x - 4*(3/2) = 4*(-22)

20x + 21x - 6 = -88
41x - 6 = -88
41x = -82
x = -2

And now that we know the value of x, we can find y.
y = (21/4)x - (1/2)
y = (21/4)*-2 - (1/2)
y = -21/2 - (1/2)
y = -22/2
y = -11

The last step should always be to CHECK your answer. Are both of the original equations true when x = -2 and y = -11? I'll leave the check to you.
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