Question

I need help with this I'll 10 points if you do it
y=x-4
y=-1/6x+3

Answer 1

`\boxed{x = (42)/(5), y = (22)/(5)}`

Explanation:

The two equations are:

`y = x - 4`

`y = (1)/(6)x + 3`

Since the left side is y in both equations, we can set the right sides equal to each other and solve for x

`x - 4 = (1)/(6)x + 3\\\\`

Multiply throughout by 6 to get rid of the denominator:

`6(x - 4) = 6((1)/(6)x + 3)`

Expand brackets on both sides:

`6x - 24 = 1x + 18`

Subtract 1x from both sides:

`\rightarrow 6x - 1x - 24 = 1x - 1x + 18\\\\\rightarrow 5x - 24 = 18\\\\`

Add 2 to both sides:

`\rightarrow 5x - 24 + 24 = 18 + 24\\\\\rightarrow 5x = 42\\\\`

Divide by 5 both sides

`(5x)/(5) = (42)/(5)\\\\x = (42)/(5)`

Substitute this value of x in either equation to find y

Choose equation (1)

`\rightarrow y = (42)/(5) - 4\\`

Multiply throughout by 5

`5y = 5 \cdot (42)/(5) - 5 \cdot 4\\\\5y = 42 - 20\\\\5y = 22\\\\y = (22)/(5)\\`

Answer:

`x = (42)/(5), y = (22)/(5)`