Question

How do you graph these systems of equations y=6x-3 and y=-1/6x+7

Answer 1

Explanation:

Go to -3 on the y axis then go up 6 to the right on and so on then go to 7 on the y axis and go down 1 to the right 6 and so on.

Answer 2

Answer: See the figure.

Explanation:

The Slope-intercept form of the equation of the line is:

`y=mx+b`

Where:

m: the slope

b: the intersection of the line with the y-axis.

Both equations in the system of equations has this form, therefore, you can know that:

`y=6x-3`

Has:

`m=6\\b=-3`

`y=-(1)/(6)x+7`

Has:

`m=-(1)/(6)\\b=7`

You can find the intersection with the x-axis by substituting y=0 and solving for x:

For the line
`y=6x-3` :

`0=6x-3\\3=6x\\(3)/(6)=x\\\\ x=(1)/(2)\\`

For the line
`y=-(1)/(6)x+7`:

`0=-(1)/(6)x+7\\-7=-(1)/(6)x\\(-6)(-7)=x\\x=42`

Therefore, knowing the intersection of each line with the y-axis and the intesrection with the x-axis, you can graph both lines, obtaining the graph shown attached.

The point of intersection of this lines is the solution of the system of equations, as you can observe in the graph.Therefore:

`x=1.622\\y=6.73`