Question 680607
Starting with y = {{{-1/2}}}x - 4
the y intercept is -4
Plot (0, -4)
the x intercept is where y = 0
0 = {{{-1/2}}}x - 4
4 = {{{-1/2}}}x 
x = 4(-2)
x = -8
Plot (-8, 0)
Draw a line through the intercepts.
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Using y = {{{3/2}}}x + 12
the y intercept is 12
Plot (0, 12)
the x intercept is where y = 0
0 = {{{3/2}}}x + 12
-12 = {{{3/2}}}x
x = -12{{{2/3}}}
x = {{{-24/3}}} = -8
Plot (-8, 0)
Draw a line through the intercepts
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Both lines will intersect and that point of intersection is the solution to this system of equations.
From the intercepts we see that both have (-8, 0) as an x intercept and this is the point where the two lines intersect.
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Therefore the solution is (-8,0)
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To confirm algebraically, put the equations equal to each other
{{{(-1/2)x-4 = (3/2)x + 12}}} and solve for x
{{{(-1/2)x - (3/2)x = 12 + 4}}}
{{{(-4/2)x = 16}}}
-2x = 16
x = -8
Plug -8 into either equation and solve for y
y = {{{(-1/2)(-8) - 4 = 4 - 4 = 0}}}
(-8,0)
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{{{graph(300,200,-10,4,-10,14,(-1/2)x-4,(3/2)x+12)}}}
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