Question 515347
First, you have to recognize that you have linear equations.
The addition and subtraction property of equality is that:
if a = b, then a+c = b+c, and a-c = b-c.
You often use this property in solving problems.
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2x + y = 6
y -x = -3
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rearranged...
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2x + y = 6
-x +y = -3
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subtract the 2nd equation from the 1st and you get:
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3x = 9
x = 3
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substitute x=3 to find y
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2x + y = 6
2(3) + y = 6
6 + y = 6
y = 0
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So, the lines intersect at:  (3,0)
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Or you could have solved by elimination.
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Gien y-x =-3
y -x+x = -3+x  (the addition property)
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y = -3+3 = 0
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substitute y=0 to find x
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2x +y = 6
2x +0 = 6
2x = 6
x = 3
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Again, this tells us the lines intersect at (3,0).
Another way of saying this is that the point (3,0) satisfies both equations.
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To graph it is easiest to use the slope-intercept form:
2x + y = 6
y -x = -3
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which become
y = -2x +6
y = x-3
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In this graph the first equation is red and the second is green.
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{{{ graph(500,500,-10,10,-10,10,-2*x+6,x-3) }}}