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laiz [17]
3 years ago
5

How many solutions does the system formed by x-y=3 and ay-ax+3a=0 have for a nonzero number a? Explain.

Mathematics
1 answer:
RoseWind [281]3 years ago
4 0
There's no solution that is nonzero.
x-y=3
x = 3+y

Substitute that to the second equation.
ay-a(3+y)+3a=0
6a=0
a=0

y = x-3

Substitute that to the second equation
a(x-3)-ax+3a=0
0 = 0
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\huge{ \boxed{ \bold{ \sf{y =  - 2x + 6}}}}

☥ \tt{Question} :

  • Write the equation of a line in slope - intercept form that has a slope of -2 and passes through the point ( - 1 , 8 ).

☥ \tt{Step  -  \: by \:  -  \: step \: explanation}

☪ \underline{ \underline{ \text{Given : }}}

  • Slope ( m ) = -2
  • Given point = ( - 1 , 8 )

☪ \underline {\underline{ \text{To \: find}}} :

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Let the point ( -1 , 8 ) be ( x₁ , y₁ )

☪ \underline{ \underline{ \text{Solution}}} :

\underline{ \sf{y - y1 = m(x - x1)}}

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↦ \text{y - 8 =  - 2 \{ x - ( - 1) \} }

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And we're done !

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♡ Have a wonderful day / night ツ

~TheAnimeGirl ♪

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