Question

10. Does the system of equations 3x - 4y = 10 and y = 3/4x + 3 have onesolution, infinitely many solutions, or no solution? *O one solutioninfinitely many solutionsno solution

Answer 1

Given the equations:

`\begin{gathered} (1)3x-4y=10 \\ (2)y=(3)/(4)x+3 \end{gathered}`

To solve the system, follow the steps below.

Step 01: Write the equations in the slope-intercept form.

An equation in the slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

So, let's write the first equation using this form. To do it, let's subtract 3x from both sides.

`\begin{gathered} 3x-4y-3x=10-3x \\ -4y=-3x+10 \end{gathered}`

Now, let's divide both sides by -4.

`\begin{gathered} (-4)/(-4)y=(-3x+10)/(-4) \\ y=(3)/(4)x-(10)/(4) \end{gathered}`

The second equation is already in the slope-intercept form.

Step 02: Compare both equations.

`\begin{gathered} (1)(3)/(4)x-(10)/(4) \\ (2)(3)/(4)x+3 \end{gathered}`

As can be seen, both have the same slope and different y-intercepts.

It is known that parallel lines have the same slope and different y-intercepts.

So, the lines are parallel.

A system of parallel lines has no solution since the lines do not have an interception point.

Answer: No solution.