−3x−9y=−12
−3x+7y=4
solve for x

Answer:

[tex] \huge{ \boxed{ \boxed{ \sf{ \red{ \sf{x = 1}}}}}}[/tex]

Step - by - step explanation :

[tex] \underline{ \underline{ \sf{Solution}}} : [/tex]

USING ELIMINATION METHOD :

[tex] \sf{ - 3x - 9y = - 12}[/tex] ••••••• equation ( i )

[tex] \sf{ - 3x + 7y = 4}[/tex] ••••••• equation ( ii )

Subtracting equation ( ii ) from ( i )

Note that while subtracting equation ( ii ) from ( i ) , sign of each term of equation ( ii ) changes and hence becomes 3x - 7y = -4.

[tex] \sf{ \cancel{ - 3x} - 9y = - 12}[/tex]

[tex] \sf{ \cancel{3x} - 7y = - 4}[/tex]

_____________________

➺ [tex] \sf{ - 16y = - 16}[/tex]

➺ [tex] \sf{ \frac{ - 16y}{ - 16} = \frac{ - 16}{ - 16}} [/tex]

➺ [tex] \sf{y = 1}[/tex]

The value of y is 1. Since , we are asked to find the value of x , substituting the value of y in equation ( i) , we get :

➺ [tex] \sf{ - 3x - 9 \times 1 = - 12}[/tex]

➺ [tex] \sf{ - 3x - 9 = - 12}[/tex]

➺ [tex] \sf{ - 3x = - 12 + 9}[/tex]

➺ [tex] \sf{ - 3x = - 3}[/tex]

➺ [tex] \sf{ \frac{ - 3x}{ - 3} = \frac{ - 3}{ - 3}} [/tex]

➺ [tex] \sf{ x = \boxed{ \bold{ \red{ \sf{1}}}}}[/tex]

Hence , the value of x is 1 .

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☞ [tex] \underline{ \sf{Extra \: Info}} : [/tex]

There are many methods to solve such simultaneous equations. They are :

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✑ Learn more :

Solve system of equations using elimination method :

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Hope I helped ! ツ

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