Answer: x = 5/3 and y = 0
note: the fraction 5/3 approximates to 1.667
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Work Shown:
Add the equations straight down. Notice how the x terms and y terms line up nicely.
Adding up the x terms straight down gives: 3x+3x = 6x
Then adding the y terms gives: 4y + (-4y) = 4y-4y = 0y = 0, so the y terms cancel out
Finally adding the '5's on the right hand side of each equation gives: 5+5 = 10
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After those those three sets of additions, we end up with this new simpler equation: 6x = 10
To isolate x, we divide both sides by 6
6x = 10
6x/6 = 10/6
x = 10/6
x = 5/3 .... divide both parts by 2 to reduce
The answer for x as a fraction is x = 5/3 which approximates to x = 1.667
Use this x value to find y
3x + 4y = 5
3(5/3) + 4y = 5 ... replace x with 5/3
5 + 4y = 5
4y = 0 .... subtract 5 from both sides
y = 0 .... divide both sides by 4
So when x = 5/3, it leads to y = 0
These two values pair up to form the solution to the system.
If you were to graph the two lines, then they would cross at the approximate location (1.667, 0)
