SOLUTION: Find the coordinates of the points of intersection of the following pair of non-parallel lines: 2x + 4y = 10 6y - 3x + 9 = 0

Algebra ->  Coordinate-system -> SOLUTION: Find the coordinates of the points of intersection of the following pair of non-parallel lines: 2x + 4y = 10 6y - 3x + 9 = 0       Log On


   

Question 389036: Find the coordinates of the points of intersection of the following pair of non-parallel lines:
2x + 4y = 10
6y - 3x + 9 = 0
Found 2 solutions by Fombitz, gwendolyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2x+%2B+4y+=+10
1.x%2B2y=5
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6y+-+3x+%2B+9+=+0
2.-x%2B2y=-3
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Add the equations together to eliminate x.
x%2B2y-x%2B2y=5-3
4y=2
highlight%28y=1%2F2%29
Then use either equation to solve for x.
x%2B2%281%2F2%29=5
x%2B1=5
highlight%28x=4%29
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Graphical verification
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Answer by gwendolyn(128) About Me  (Show Source):
You can put this solution on YOUR website!
For a pair of non-parallel lines, there should be one point of intersection. This is the same as solving for the the unknowns (x, y) in the pair of equations.
We have two equations and two unknowns (variables), so we should be able to solve for the unknowns using substitution.
Let's find the value of x in the first equation (we could choose y but we picked x at random).
2x + 4y = 10
2x + 4y - 4y = 10 - 4y
2x = 10 - 4y
Dividing each side by 2:
(2x)/2 = (10 - 4y)/2
x = 5 - 2y
Now we substitute this value for x into the second equation:
6y - 3x + 9 = 0
6y - 3*(5 - 2y) + 9 = 0
6y + (-3)*(5 - 2y) + 9 = 0
And distribute the -3:
6y + (-3)*5 + (-3)(-2y) + 9 = 0
6y - 15 + 6y + 9 = 0
12y - 6 = 0
12y = 6
Dividing each side by 12:
(12y)/12 = (6)/12
y = 1/2

And, plugging our value for y back into expression for x:
x = 5 - 2*(1/2)
x = 5 - 1
x = 4
So, there is one point of intersection at (4, 1/2)