Question

A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?

Answer 1

"They have different slopes but the same y-intercept, so they have one solution" is the statement which best describes the two lines.

Answer: Option D

Step-by-step explanation:

Given equations:

           $y=\left(\frac{1}{2} \times x\right)-3$

           $y=\left(-\frac{1}{2} \times x\right)-3$

As we know that the slope intercept form of a line is  

                             y = m x + c  

So, from equation 1 and equation 2 we can see that

              $m_{1}=\frac{1}{2} \quad \text { and } c_{1}=-3$

              $m_{2}=-\frac{1}{2} \text { and } c_{2}=-3$

So, from the above expressions, we can say that both lines have different slopes but have same y – intercept with one common solution when x = 0.

Answer 2

Answer: D

Step-by-step explanation: