Question

Solve the following system of equations graphically; $4x-5y+16=0$; $2x+y-6=0$. Determine the vertices of the triangle formed by the lines and the x-axis.

Answer 1

We have system of equation:

$A:4x-5y+16=0---\left(1\right)$

$B:2x+y-6=0----\left(2\right)$

For $A$

$x0-41$

$y16/504$

For $B$

$x031$

$y604$

From solving equation $\left(1\right)$ & $\left(2\right)$, we get only one point $(1,4)$ as

$\frac{4x-5y+16=04x+2y-12=0--+}{-7y+28=0\Rightarrow y=4},x=\frac{6-y}{2}=\frac{2-4}{2}=1$

So, the vertices are $(-4,0),(1,4)$ & $(3,0)$