Question

A system of equations is given below.

y = negative 3 x + 6 and y = 6 minus 3 x
5
Which of the following statements best describes the two lines?
A They have different slopes and different y-intercepts, so they have no solution.
B They have different slopes and different y-intercepts, so they have one solution.
C They have the same slope and the same y-intercept, so they have no solution.
D They have the same slope and the same y-intercept, so they have infinitely many solutions.

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A system of equations is given below.

y = - 3x + 6 and y = 6 - 3x

Which of the following statements best describes the two lines

A. They have different slopes and different y-intercepts, so they have no solution.

B. They have different slopes and different y-intercepts, so they have one solution.

C. They have the same slope and the same y-intercept, so they have no solution.

D. They have the same slope and the same y-intercept, so they have infinitely many solutions.

CONCEPT TO BE IMPLEMENTED

The general equation of any line is

ax + by + k = 0

Which can be rewritten as

y = mx + c

Where m = slope of the line and c is the y - intercept of the line

EVALUATION

Here the given system of equations are

$\sf{y = - 3x + 6 \: \: \: and \: \: \: y = 6 - 3x}$

So the slope of both the lines = - 3 & y - intercept of both the lines = 6

Hence the given system of equations have the same slope and the same y-intercept, so they have infinitely many solutions

FINAL ANSWER

Hence the correct option is

D. They have the same slope and the same y-intercept, so they have infinitely many solutions

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Answer 2

Solution ⤵️

To Find ⤵️

Choose the correct option:-

A system of equations is given below.

y = - 3x + 6 and y = 6 - 3x

Which of the following statements best describes the two lines:-

A. They have different slopes and different y-intercepts, so they have no solution.

B. They have different slopes and different y-intercepts, so they have one solution.

C. They have the same slope and the same y-intercept, so they have no solution.

D. They have the same slope and the same y-intercept, so they have infinitely many solutions.

Concept to be used ⤵️

The general equation of any line is,

ax + by + k = 0

Which can be rewritten as,

y = mx + c

Where m = slope of the line and c is the y - intercept of the line

Calculation ⤵️

Given system of equations are:-

$\sf{y = - 3x + 6 \: \: \: and \: \: \: y = 6 - 3x}$

So the slope of both the lines = - 3 & y - intercept of both the lines = 6

Hence the given system of equations have the same slope and the same y-intercept, so they have infinitely many solutions

Your Answer⤵️

Therefore the correct option is :-

Option D. They have the same slope and the same y-intercept, so they have infinitely many solutions.

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