Question 572454: 2x-8y=7
5x+4y=5
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! You don't specify what method to use to solve this equation, so lucky me! I get to pick!!! :-)
These don't lend themselves to substitution, so I'm going to use the other method. (Elimination?)
2x - 8y = 7
5x + 4y = 5
I'm going to try to eliminate the y term in both of these. To do that, I need the same factor on the y term, so ...
2x - 8y = 7 (unchanged from above)
2(5x + 4y) = 2(5) multiply both sides by 2 giving ...
10x + 8y = 10
Now let me rewrite the equations using this adjusted 2nd equation:
2x - 8y = 7
10x + 8y = 10 Add these together and ...
12x = 17
Divide both sides by 12 (yucky)
x = 17/12 (Are you sure you copied this down correctly?)
2(17/12) - 8y = 7
17/6 - 8y = 7
Add 8y to both sides:
17/6 = 7 + 8y
Multiply both sides by 6
17 = 6(7+8y)
17 = 42 + 48y
Subtract 42 from both sides:
-25 = 48y
Divide both sides by 48
-25/48 = y (yucky yucky yucky - my very technical term)
Checking:
1st equation:
2(17/12) -8(-25/48) = 7
Factoring out a 2 from numerator and denominator of first term:
17/6 - 8(-25/48) = 7 now getting rid of the double negative in the 2nd term:
17/6 + 8(25/48) = 7
Factoring out an 8 from the numerator and denominator of 2nd term:
17/6 + 25/6 = 7
42/6 = 7
7 = 7 Correct!
2nd equation:
5(17/12) + 4(-25/48) = 5 We can factor a 4 from numberator and denominator in 2nd term:
5(17/12) + (-25/12) = 5
85/12 - 25/12 = 5
60/12 = 5
5 = 5 Correct!
Whew! That was ugly, but it worked out in the end. Hope you were able to follow. These messy ones can be confusing if we're not doing them together.
Good luck!! Come back for more some time. :-)
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