Question 286125: finding x,y the questionis x+2y=4 2x-y=3 I don't understand when finding 2x
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The notion of '2x' is simply 2 times x, but I doubt that is what you mean...
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Consider the two linear equations as a system of simultaneous equations.
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Usually, you are looking for their point of intersection, or at least if they intersect or not.
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x + 2y =4
2x -y = 3
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Multiply the second equation by 2 to be able to eliminate the 'y' terms.
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2(2x-y)=2(3)
4x - 2y = 6
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Substitute this equation for the second equation and add them.
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x + 2y =4
4x - 2y = 6
5x = 10
x = 2
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Substitute x=2 into the the first equation to find y.
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x + 2y =4
2 + 2y =4
2y = 2
y = 1
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Now we have defined the point (2,1).
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We can substitute both values into the second equation to see if they are correct.
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2x -y = 3
2*2 -1 = 3
Correct.
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And you can graph it to see that they cross at (2,1). For this step having both equations in slope-intercept form is best for picking points to draw the lines: y = mx+b
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x + 2y =4
2y = -x + 4
y = (-1/2)x + 2
m = slope = -1/2
b = y -intercept = 2, which is the point (0,2)
x -intercept is where y=0, so we solve: 0 = (-1/2)x + 2, so x=4, which is the point (4,0)
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2x -y = 3
-y = -2x + 3
Multiply both sides by -1.
y = 2x - 3
m = slope = 2
b = y-intercept = -3, which is the point (0,-3)
x-intercept = 0 = 2x - 3, x = 3/2, which is the point (3/2,0)
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Note that we can tell the two lines are perpendicular because their slopes are negative reciprocals.
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