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3 years ago

When using substitution to solve a system of equations , how can you tell when a system has no solution

Mathematics

1 answer:

tatuchka [14]3 years ago

3 0

Answer:

If you have a false statement at the end.

Step-by-step explanation:

When using substitution to solve a system of equations, you can tell when the system has no solution if the equation at the end produces a false statement.

For example, at the end if you have something like 3x + 1 = 3x - 4. You would subtract 3x from both sides of the equation and be left with 1 = -4.

This is a false statement, 1 does NOT equal -4. Therefore, system of equations has no solution.

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Read 2 more answers

Find the points having x-coordinate of 9 whose distance from the point (3,-2) is 10.

kotegsom [21]

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{y})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{d}{10}=\sqrt{[9-3]^2+[y-(-2)^2]}\implies 10=\sqrt{(9-3)^2+(y+2)^2} \\\\\\ 10=\sqrt{6^2+\stackrel{FOIL}{(y^2+4y+4)}}\implies 10^2=36+(y^2+4y+4)$

$\bf 100=y^2+4y+40\implies 0=y^2+4y-60 \\\\\\ 0=(y+10)(y-6)\implies y= \begin{cases} -10\\ 6 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (9,-10)\qquad (9,6)~\hfill$

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4 years ago

Point P'P′P, prime is the image of P(6,0)P(6,0)P, left parenthesis, 6, comma, 0, right parenthesis under the translation (x,y)\t

gtnhenbr [62]

The location of point P is at (0, -1)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point left, right, up or down in the coordinate plane.

We are given the coordinates of point P and asked to find the coordinates of the image P'.

Given point P at P(6, 0), A translation of (x,y)→(x−6,y−1) is done to produce an image P'. Therefore point P is translated 6 units left and 1 unit down to get P'.

Hence P' = (0, -1)

Therefore P' is at (0, -1)

Find more at: brainly.com/question/15639127

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3 years ago