Question 336265
1.{{{x+y=11}}}
2.{{{x-y=1}}}
Solve them algebraically by adding them together to eliminate {{{y}}}.
{{{x+y+x-y=11+1}}}
{{{2x=12}}}
{{{highlight(x=6)}}}
Then go back and use either equation to solve for {{{y}}}.
{{{6+y=11}}}
{{{highlight(y=5)}}}
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You can solve it graphically by plotting the graphs and looking for the intersection point.
To plot each line, find the intercepts.
To find the x-intercept, set y=0 and solve for x.
{{{x+y=11}}}
{{{x+0=11}}}
{{{x=11}}}
(11,0)
Plot it.
{{{drawing(300,300, -2,12,-2,12, grid(1),
circle(11,0,0.4),
graph(300,300, -2,12,-2,12, 0))}}}
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To find the y-intercept, set x=0 and solve for y.
{{{x+y=11}}}
{{{0+y=11}}}
{{{y=11}}}
(0,11)
Plot it too.
{{{drawing(300,300, -2,12,-2,12, grid(1),
circle(11,0,0.4),
circle(0,11,0.4),
graph(300,300, -2,12,-2,12,0))}}}
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Connect these 2 points with the line.
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{{{drawing(300,300, -2,12,-2,12, grid(1),
circle(11,0,0.4),
circle(0,11,0.4),
graph(300,300, -2,12,-2,12, 11-x))}}}
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To find the x-intercept, set y=0 and solve for x.
{{{x-y=1}}}
{{{x-0=1}}}
{{{x=1}}}
(1,0)
{{{drawing(300,300, -2,12,-2,12, grid(1),
circle(11,0,0.4),
circle(0,11,0.4),
circle(1,0,0.4),
graph(300,300, -2,12,-2,12, 11-x))}}}
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To find the y-intercept, set x=0 and solve for y.
{{{x-y=1}}}
{{{0-y=1}}}
{{{y=-1}}}
(0,-1)
{{{drawing(300,300, -2,12,-2,12, grid(1),
circle(11,0,0.4),
circle(0,11,0.4),
circle(1,0,0.4),
circle(0,-1,0.4),
graph(300,300, -2,12,-2,12, 11-x))}}}
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Connect these 2 points with the line.
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{{{drawing(300,300, -2,12,-2,12, grid(1),
circle(11,0,0.4),
circle(0,11,0.4),
circle(1,0,0.4),
circle(0,-1,0.4),
circle(6,5,0.3),
circle(6,5,0.2),
circle(6,5,0.1),
circle(6,5,0.05),
graph(300,300,-2,12,-2,12, 11-x,x-1))}}}
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Guess what, the intersection point is ({{{6}}},{{{5}}}).
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Now you have no excuses for not passing.