SOLUTION: solve and determine whether each system has no solution, one solution or an infinite number of solutions show why y=4x+6 8x-y= -7

Algebra ->  Linear-equations -> SOLUTION: solve and determine whether each system has no solution, one solution or an infinite number of solutions show why y=4x+6 8x-y= -7      Log On


   

Question 243280: solve and determine whether each system has no solution, one solution or an infinite number of solutions show why
y=4x+6
8x-y= -7
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
y = mx + b is the basic linear equation.
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EQ 1: y = 4x + 6, which is already in this form.
m = 4, which is the slope
y-intercept = 6
x-intercept = -3/2, which can be demonstrated by 4*(-3/2) + 6 = 0
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EQ 2: 8x - y = -7, which needs to be shaped up algebraically.
Add y to both sides
8x = -7 + y = y - 7
Add 7 to both sides
8x + 7 = y
y = 8x + 7
m = 8, which is twice a great a slope as EQ 1
y-intercept = 7
x-intercept = -7/8
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Now graph the two equations.
%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4%2Ax%2B6%2C+8%2Ax%2B7%29%0D%0A
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There is one solution, as can be seen in the graph.
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To demonstrate algebraically there is one solution, recall that equal things are equal. y=y is self-evident, so you can set the two equations equal to one another and solve them.
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8x + 7 = 4x + 6
Subtract 4x from both sides
4x + 7 = 6
Subtract 7 from both sides
4x = -1
Divide both sides by 4
x = -1/4
So x=-1/4 is the solution (the unique point where the two equations cross).