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3 years ago

15

Which of the following equations results in no solutions?

1 answer:

agasfer [191]3 years ago

4 0

Answer choice B would result in no solution

Hope this helps ;)

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murzikaleks [220]

Answer:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Step-by-step explanation:

Slope-intercept form of a <u>linear equation</u>:

$\boxed{y=mx+b}$

where:

m is the slope.
b is the y-intercept (where the line crosses the y-axis).

<u>Slope formula</u>

$\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}$

<u>Equation 1</u>

<u />

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(-1, 6)$

$\textsf{Let }(x_2,y_2)=(0, 1)$

<u>Substitute</u> the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5$

From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=-5x+1$

<u>Equation 2</u>

<u />

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(1, 1)$

$\textsf{Let }(x_2,y_2)=(0, -4)$

<u>Substitute</u> the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5$

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=5x-4$

<u>Conclusion</u>

Therefore, the system of linear equations shown by the graph is:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Learn more about systems of linear equations here:

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