Question 124889
I'll do the first two to get you started


# 1


Start with the given system of equations:


{{{1x-y=3}}}

{{{1x+y=5}}}





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


{{{1x-y=3}}} Start with the given equation



{{{-y=3-x}}}  Subtract {{{ x}}} from both sides



{{{-y=-x+3}}} Rearrange the equation



{{{y=(-x+3)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=(-1/-1)x+(3)/(-1)}}} Break up the fraction



{{{y=x-3}}} Reduce



Now lets graph {{{y=x-3}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)



{{{ graph( 600, 600, -10, 10, -10, 10, x-3) }}} Graph of {{{y=x-3}}}




So let's solve for y on the second equation


{{{1x+y=5}}} Start with the given equation



{{{1y=5-x}}}  Subtract {{{ x}}} from both sides



{{{1y=-x+5}}} Rearrange the equation



{{{y=(-x+5)/(1)}}} Divide both sides by {{{1}}}



{{{y=(-1/1)x+(5)/(1)}}} Break up the fraction



{{{y=-x+5}}} Reduce




Now lets add the graph of {{{y=-x+5}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, x-3,-x+5) }}} Graph of {{{y=x-3}}}(red) and {{{y=-x+5}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{4}}},{{{1}}}) (note: you might have to adjust the window to see the intersection)





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# 2






Start with the given system of equations:


{{{3x+y=5}}}

{{{1x-2y=4}}}





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


{{{3x+y=5}}} Start with the given equation



{{{1y=5-3x}}}  Subtract {{{3 x}}} from both sides



{{{1y=-3x+5}}} Rearrange the equation



{{{y=(-3x+5)/(1)}}} Divide both sides by {{{1}}}



{{{y=(-3/1)x+(5)/(1)}}} Break up the fraction



{{{y=-3x+5}}} Reduce



Now lets graph {{{y=-3x+5}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)



{{{ graph( 600, 600, -10, 10, -10, 10, -3x+5) }}} Graph of {{{y=-3x+5}}}




So let's solve for y on the second equation


{{{1x-2y=4}}} Start with the given equation



{{{-2y=4-x}}}  Subtract {{{ x}}} from both sides



{{{-2y=-x+4}}} Rearrange the equation



{{{y=(-x+4)/(-2)}}} Divide both sides by {{{-2}}}



{{{y=(-1/-2)x+(4)/(-2)}}} Break up the fraction



{{{y=(1/2)x-2}}} Reduce




Now lets add the graph of {{{y=(1/2)x-2}}} to our first plot to get:


{{{ graph( 600, 600, -10, 10, -10, 10, -3x+5,(1/2)x-2) }}} Graph of {{{y=-3x+5}}}(red) and {{{y=(1/2)x-2}}}(green)


From the graph, we can see that the two lines intersect at the point ({{{2}}},{{{-1}}}) (note: you might have to adjust the window to see the intersection)