SOLUTION: need help with 7x/3 + 5y/4=4 5x/6 - 2y=21
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Question 253103: need help with 7x/3 + 5y/4=4 5x/6 - 2y=21
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.
Multiply both sides by the LCD to clear any fractions.
Distribute and multiply.
----------------------------------------------------------------------------
Move onto the second equation.
Multiply both sides by the LCD to clear any fractions.
Distribute and multiply.
----------------------------------------------------------------------------
So we now have the system of equations
and it turns out that the solution to that system above is the same solution to the original system of equations.
Start with the given system of equations:
Multiply the both sides of the first equation by 4.
Distribute and multiply.
Multiply the both sides of the second equation by 5.
Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms.
Simplify.
Divide both sides by to isolate .
Reduce.
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Multiply.
Subtract from both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So the solutions are and .
Which form the ordered pair )
.
This means that the system is consistent and independent.
Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.
Graph of (red) and (green)
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Two lines that meet at (6,-8)
7x/3 + 5y/4=4
5x/6 - 2y=21
multiply the both of them by 6
14x+30y/4=24
5x-12y=126
multiply the first by 2
28x+15y=48
5x-12y=126
solve one of them for x in terms of y
5x=126+12y
x=126/5+12y/5
substitute that for x in the first
28*(126/5+12y/5)+15y=48
A little messy but it does come down to
y=-8
substitute -8 for y in either of the original
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