Question 68645
{{{ 3I[1]-4I[2]=17 and I[1]+3I[2]=-3 }}}
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Let us represent other variables.
{{{x = I[1]}}}
{{{y = I[2]}}}
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Rewrite the equations
3x-4y=17 
x+3y=-3
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We can solve for the variables using elimination method.
Multiply -3 to x+3y=-3
3x - 4y = 17
-3x - 9y = 9
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Add the two equations
-13y = 26
<br>Divide -13 both sides
y = -2  <<<<<<<<<<<<<<<{{{y = I[2]}}}
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Substitute 2 for y in either equation. Solve for x.
x+3y=-3, y = 2
x + 3(-2)= -3
x - 6 = -3
x = 3  <<<<<<<<<<<<<< {{{x = I[1]}}}

<br> Checking: 

3x-4y=17 , x = 3, y = -2
3(3) - 4(-2) = 17
9 + 8 = 17
17 = 17 ----------->> True
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x+3y=-3, x = 3, y = -2
3 + 3(-2) = -3
3 -6 = -3
-3 = -3 --------->> True