Question

does the system have one solution no solution or an infinite number of solutions?4x + 3y =524x + 3y =7choose the correct answer belowa. infinitely many solutionsb. one solutionc. no solution

Answer 1

The Slope-Intercept form of an equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

- The first equation given in the exercise is:

`4x+3y=5`

Solve for "y" in order to write it in Slope-Intercept form:

`\begin{gathered} 3y=-4x+5 \\ y=-(4)/(3)x+(5)/(3) \end{gathered}`

You can identify that:

`\begin{gathered} m_1=-(4)/(3) \\ \\ b_1=(5)/(3) \end{gathered}`

- The second equation is:

`24x+3y=7`

Solve for "y":

`\begin{gathered} 3y=-24x+7 \\ \\ y=(-24)/(3)x+(7)/(3) \\ \\ y=-8x+(7)/(3) \end{gathered}`

You can identify that:

`\begin{gathered} m_2=-8 \\ \\ b_2=(7)/(3) \end{gathered}`

- As you can notice, the lines are not parallel, because:

`m_1\\e m_2`

- The lines are not the the same line, because:

`\begin{gathered} m_1\\e m_2 \\ b_1\\e b_2 \end{gathered}`

- Therefore, since they are different ant they're not parallel, they will intersect each other at some point. This means that the System of equations has one solution.

The answer is: Option b.