Question

How many solution does the system of equations below have?y = 6x - 5y = -4/5x - 2/3No solutionOne solutionInfinitely many solutions

Answer 1

To find the number of solutions that have a system of linear equation as given:

`\begin{gathered} y=6x-5 \\ y=-(4)/(5)x-(2)/(3) \end{gathered}`

You need to identify the slope of each equation.

`y=mx+b`

m is the slope

If the equations have the same slope, there is not solution as the lines are parallel and don't intersects each other.

If the equations have different slopes, there is one solution as the lines intersect each other in one point.

If the equations are the same (have the same slope and y- intercept) the solutions are infinite as the lines are equal.

For the given equations you have the next slopes:

First equation: m= 6

Second equation: m=-4/5

As the equations have different slopes, there are one solution for the system