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

Jun 23, 2018

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 $x = 0$

$y = \frac{1}{2} \cdot 0$

$y = 0$ or $\left(0 , 0\right)$

Second Point: For $x = 2$

$y = \frac{1}{2} \cdot 2$

$y = 1$ or $\left(2 , 1\right)$

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 $\left(0 , 3\right)$

Second Point: For $x = 3$

$y = - 3 + 3$

$y = 0$ or $\left(3 , 0\right)$

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 $\left(2 , 1\right)$

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