How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution

Mathematics

1 answer:

AveGali [126]3 years ago

6 0

Answer:

One

Step-by-step explanation:

It is given that,

y = 3x-5 ....(1)

y = -x+4 .....(2)

We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,

$3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}$

Put the value of x in equation (1) we get :

$y = 3x-5\\\\y = 3\times \dfrac{9}{4}-5\\\\y=\dfrac{7}{4}$

It means that the value of x is $\dfrac{9}{4}$ and the value of y is $\dfrac{7}{4}$ . Hence, the given equations has only one solution.

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Before dilation:
the height of the triangle is h₁ = 7 - (-1) = 8
the width of the triangle is w₁ = 7 - (-5) = 12

After dilation:
the height of the is h₂ = 9-7 = 2
the width of the triangle is w₂ = -5 - (-8) = 3

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Also, the scale factor is w₂/w₁ = 3/12 = 1/4 = 0.25

Answer: The scale factor is 0.25