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3 years ago

A system of linear equations contains two equations with the same slope. Select all of the correct statements.

2 answers:

5 0

B. The system may represent two parallel lines and have no solution.
C. The system my represent the same line and have infinitely many solutions.

lina2011 [118]3 years ago

4 0

Answer:

B and C are correct statements.

Step-by-step explanation:

Given is : A system of linear equations contains two equations with the same slope.

If the two given linear equations have the same slope but different y intercept, then the lines will be parallel. As we know that the parallel lines never meet or intersect, so such equations will have no solution.

Hence, B. The system may represent two parallel lines and have no solution. - is true.

Also if the given equations have same slope and same y intercept then it is the same line with infinite number of solutions.

Therefore, option C. The system may represent the same line and have infinitely many solutions. - is also true.

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Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).

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The equation of the line is $y=\frac{1}{4}x-\frac{29}{7}$

Explanation:

The equation of the line is perpendicular to $y=-14 x-8$

The equation is of the form $y=mx+b$ where m=-14

Slope:

The slope of the perpendicular line can be determined using the formula,

$m_1 \cdot m_2=-1$

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$m_2=\frac{1}{14}$

Thus, the slope of the line is $m=\frac{1}{14}$

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the slope $m=\frac{1}{14}$ and the point (2,-4), we get,

$y+4=\frac{1}{14}(x-2)$

Simplifying, we get,

$y+4=\frac{1}{14}x-\frac{1}{7}$

$y=\frac{1}{14}x-\frac{1}{7}-4$

$y=\frac{1}{4}x-\frac{29}{7}$

Thus, the equation of the line is $y=\frac{1}{4}x-\frac{29}{7}$

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