Solve the system using substitution.

Mathematics

1 answer:

miv72 [106K]3 years ago

6 0

Substitution method is one of the ways to solve this system.

-5x+y=4 and 4x-4y=16.

First we will divide the second equation with number 4 and get

x-y=4 => x=y+4 than we will replace x in the first equation

-5(y+4)+y=4 => -5y-20+y=4 => -4y=4+20 => -4y=24 => y=-6

x-(-6))=4 => x+6=4 => x=4-6=-2 (x,y)=(-2,-6)

Good luck!!!

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the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of t

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Answer: $y = 2x -6$

Step-by-step explanation:

Since, If (x,y) represents the coordinates of a line, then after dilation about the origin by the scale factor k, the coordinates of the resultant line will get by the rule,

$(x,y)\rightarrow (kx,ky)$

Here, The equation of the given line is,

y = 2x - 4

x-intercept and y-intercept of the line are (2,0) and (0,-4) respectively,

Hence, the line y = 2x - 4 will be passes through the points (2,0) and (0,-4),

By the above property,

The dilated line about the origin will be passes through the points (3,0) and (0,-6), ( Because (3/2× 2, 3/2×0) = (3,0) and (3/2×0, 3/2×-4) = (0,-6) )

Hence, the equation of transformed line after dilation,

$y-0 = \frac{-6-0}{0-3}(x-3)$