Question

How many solutions does this linear equation have? Y= 2x - 5

Answer 1

Y = 2x - 5...slope = 2, y int = -5

-8x - 4y = -20
-4y = 8x - 20
y = -2x + 5....slope = -2, y int = 5

different slopes, different y int's means 1 solution <==

** same slope, same y int = infinite solutions
** same slope, different y int's = no solutions

Answer 2

Answer:

Our given system has exactly one solution.

Step-by-step explanation:

We have been given a system of equation. We are asked to find the number of solutions for our given system.

First of all, we will convert our second equation in slope-intercept form of equation as shown below:

$-8x-4y=-20$

Upon dividing both sides of our equation by -4, we will get:

$\frac{-8x}{-4}-\frac{4y}{-4}=\frac{-20}{-4}$

$2x+y=5$

$2x-2x+y=-2x+5$

$y=-2x+5$

Upon comparing our both equations, we can see that they have different slopes and different y-intercepts, therefore, they will have exactly one solutions as they will intersect at one place.

Upon looking at our attachment, we can see that our explanation is correct.