Question

Solve graphically: 3y= 5-x and 2x = y+3. Write down the co-ordinates of the point of intersection of the two lines.

Answer 1

y=-1/3x+5/3 and y=2x-3 and graph

Answer 2

they cross at (2,1) you can see the solution by looking

Answer 3

\[3y= 5-x\]\[2x = y+3\]
\[y=\frac{5}{3}-\frac{1}{3}x\]\[y=2x-3\]
\[\frac{5}{3}-\frac{1}{3}x=2x-3\]\[\frac{5-x}{3}=2x-3\]\[5-x=3(2x-3)\]\[5-x=6x-9\]\[7x=14\]\[x=2\]
\[y=2\times2-3\]\[y=1\]
So, the point of intersection of the two lines is (2,1).