algebra 1 question please help answers

Question

An equation is shown below:

5x - y = 8

Part A: Explain how you will show all of the solutions that satisfy this equation. (4 points)

Part B: Determine three different solutions for this equation. (4 points)

Part C: Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent. (2 points)

Answer 1

5x-y=8

This is the equation of a line.  A line has infinite solutions, so you would show all solutions by plotting a couple of points on a cartesian coordinate coordinate system and using those points to graph the line.

 

B.  To find solutions of the equation, all you have to do is pick a value for x, input that into the equation and solve for y.  This will give you a point (x,y) that is on the line

 

Let x= 0

5(0)-y=8

-y=8

y=-8

one solution is the point (0,-8)

 

Let x=1

5(1)-y=8

-y=8-5

-y=3

y=-3

One solution is the point (1,-3)

 

Let x=-1

5(-1)-y=8

-5-y=8

-y=13

y=-13

one solution is the point (-1,-13)

 

C.  In order for a sysyem of equations to be inconsistent we need to find an equation to pair with this line which will not allow for any solutions for x,y that will work for noth equations.  Remember that parallel lines have the same slope.  Any line with the same slope as 5x-y=8 but a point that is not on the line 5x-y=8 will be parallel to this line and never touch it.  This, the two equations would be inconsistent because there will be no solutions that work for both.

 

Let's put 5x-y =8 into slope intercept form of y=mx+b where m is the slope and the point (0,b) is the y intercept.

 

-y= -5x+8

y=5x-8

This has slope m=5 and y intercept at (0,-8)

 

All we have to do is write the equation of a line with slope 5 and a different y intercept

For example...

 

y= 5x+1

 

Note:  You could use any number other than -8 for b and it would be correct