How do you solve the following linear system: # 3x – 9y = 0, 3x – y = 4 #?

Answer 1

#(x,y)=(3/2,1/2)#

#3x-9y=0to(1)#
#3x-y=4to(2)#
#"from equation "(2)color(white)(x)3x=4+y#
#"substitute "3x=4+y" into equation "(1)#
#4+y-9y=0larrcolor(blue)"collect like terms"#
#rArr4-8y=0#
#"subtract 4 from both sides"#
#cancel(4)cancel(-4)-8y=0-4#
#rArr-8y=-4#
#"divide both sides by "-8#
#(cancel(-8) y)/cancel(-8)=(-4)/(-8)#
#rArry=1/2#
#"substitute "y=1/2" into equation "(2)" and solve for x"#
#3x-1/2=4#
#rArr3x=4+1/2=9/2#
#rArrx=(9/2)/3=9/2xx1/3=9/6=3/2#
#rArr"solution is "(x,y)to(3/2,1/2)#
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Answer 2

To solve the linear system:

[ \begin{cases} 3x - 9y = 0 \ 3x - y = 4 \end{cases} ]

First, solve one of the equations for one variable, then substitute this expression into the other equation.

From the second equation, isolate ( x ):

[ 3x - y = 4 \ 3x = y + 4 \ x = \frac{y + 4}{3} ]

Substitute ( x = \frac{y + 4}{3} ) into the first equation:

[ 3\left(\frac{y + 4}{3}\right) - 9y = 0 \ y + 4 - 9y = 0 \ -8y + 4 = 0 \ -8y = -4 \ y = \frac{-4}{-8} \ y = \frac{1}{2} ]

Now that we have found ( y = \frac{1}{2} ), substitute this value into one of the original equations to find ( x ):

[ 3x - 9\left(\frac{1}{2}\right) = 0 \ 3x - \frac{9}{2} = 0 \ 3x = \frac{9}{2} \ x = \frac{9}{6} \ x = \frac{3}{2} ]

So, the solution to the linear system is ( x = \frac{3}{2} ) and ( y = \frac{1}{2} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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