Question

How do you solve the system by graphing and what is the ordered pair for x - 2y = 0 and 5x+2y=24?

Answer 1

See a solution process below:

Explanation:

For each equation we can find two solutions for the equation, plot the points and draw a line through the two points to graph the line.

Equation 1

For `x = 0`

`0 - 2y = 0`

`-2y = 0`

`(-2y)/color(red)(-2) = 0/color(red)(-2)`

`y = 0` or `(0, 0)`

For `x = 4`

`4 - 2y = 0`

`-color(red)(4) + 4 - 2y = -color(red)(4) + 0`

`0 - 2y = -4`

`-2y = -4`

`(-2y)/color(red)(-2) = (-4)/color(red)(-2)`

`y = 2` or `(4, 2)`

graph{(x^2+y^2-0.25)((x-4)^2+(y-2)^2-0.25)(x-2y)=0 [-30, 30, -15, 15]}

Equation 2

For `x = 0`

`(5 * 0) + 2y = 24`

`0 + 2y = 24`

`2y = 24`

`(2y)/color(red)(2) = 24/color(red)(2)`

`y = 12` or `(0, 12)`

For `x = 2`

`(5 * 2) + 2y = 24`

`10 + 2y = 24`

`-color(red)(10) + 10 + 2y = -color(red)(10) + 24`

`0 + 2y = 14`

`2y = 14`

`(2y)/color(red)(2) = 14/color(red)(2)`

`y = 7` or `(2, 7)`

graph{(x^2+(y-12)^2-0.25)((x-2)^2+(y-7)^2-0.25)(5x+2y-24)(x-2y)=0 [-30, 30, -15, 15]}

Solution

We can see below the lines intersect at: (4, 2)

graph{(5x+2y-24)(x-2y)=0 [-12, 12, -6, 6]}