Question 679911
Starting with 2y = -3x + 4
Isolate the y variable
y = {{{(-3/2)x + 4/2}}}
{{{highlight(y=(-3/2)x+2)}}}
The y intercept is 2
Plot (0,2)
The x intercept is where y = 0
0 = {{{(-3/2)x+2}}}
-2 = {{{-3/2}}}x
-2{{{-2/3}}} = x
x = {{{4/3}}}
Plot ({{{4/3}}},0)
Draw a line through the intercepts.
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Using x = y+8
Isolate the y variable
{{{highlight_green(y = x-8)}}}
y intercept is -8
Plot (0, -8)
x intercept is where y = 0
0 = x-8
x = 8
Plot (8,0)
Draw a line through the intercepts
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The solution is the point of interception of those two lines
{{{graph(300,200,-2,10,-10,2,(-3/2)x+2, x-8)}}}
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Algebraically,
{{{(-3/2)x+2=x-9}}}
{{{2 + 9 = x + (3/2)x}}}
{{{11 = (5/2)x}}}
{{{x=22/5}}}
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Use the x value in either equation to find the y value
y = {{{22/5}}} - 9
y = {{{(22/5) - 9(5/5) = 22/5 - 45/5 = 23/5}}}
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The solution, point of intersection is ({{{22/5}}}, {{{23/5}}})
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