Question

How do you solve `y=1/2x`, `y=-x+3` by graphing?

Answer 1

See a solution process below:

Explanation:

First, solve for two points on the first equation, plot the two points and then draw a straight line through the two points:

First Point: For `x = 0`

`y = 1/2 * 0`

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

Second Point: For `x = 2`

`y = 1/2 * 2`

`y = 1` or `(2, 1)`

graph{(y - 0.5x)(x^2+y^2-0.035)((x-2)^2+(y-1)^2-0.035)=0 [-10, 10, -5, 5]}

Next, solve for two points on the second equation, plot the two points and then draw a straight line through the two points:

First Point: For `x = 0`

`y = -0 + 3`

`y = 3` or `(0, 3)`

Second Point: For `x = 3`

`y = -3 + 3`

`y = 0` or `(3, 0)`

graph{(y+x-3)(y - 0.5x)(x^2+(y-3)^2-0.035)((x-3)^2+y^2-0.035)=0 [-10, 10, -5, 5]}

We can see the lines intersect at `(2, 1)`

graph{(y+x-3)(y - 0.5x)((x-2)^2+(y-1)^2-0.035)=0 [-10, 10, -5, 5]}