Question

The graph of 3x + 2y = 6 meets the x-axis at point P and the y-axis at point Q. Use the graphical method,then the co-ordinates of points P and Q are P = (2, 0) and Q = (0, 3)
If true then enter $1$ and if false then enter $0$

Answer 1

To draw the graph for the given linear equation, we need to first plot
the points which lie on it, join them to get a straight line.
First equation is $x+y=2=>y=-x+2$
Substitute different values of x in the equation and calculate to get corresponding values of y.

$x$	$y=-x+2$	Point $(x,y)$
$0$	$2$	$(0,2)$
$2$	$0$	$(2,0)$
$4$	$-2$	$(4,-2)$
$-1$	$3$	$(-1,3)$
$-3$	$5$	$(-3,5)$

Plot these points on the graph paper and join them using a straight line.
Second equation is $x-2y=5=>y=\frac{x}{2}-\frac{5}{2}$
Substitute different values of x in the equation and calculate to get corresponding values of y.

$x$	$y=\frac{x}{2}-\frac{5}{2}$	Point $(x,y)$
$0$	$-\frac{5}{2}$	$(0,-\frac{5}{2})$
$3$	$-1$	$(3,-1)$
$5$	$0$	$(5,0)$
$-2$	$-\frac{7}{2}$	$(-2,-\frac{7}{2})$
$-3$	$-4$	$(-3,-4)$

Plot these points on the graph paper and join them using a straight line.
Third equation is $\frac{x}{3}+y=0=>y=-\frac{x}{3}$
Substitute different values of x in the equation and calculate to get corresponding values of y.

$x$	$y=-\frac{x}{3}$	Point $(x,y)$
$0$	$0$	$(0,0)$
$3$	$-1$	$(3,-1)$
$6$	$-2$	$(6,-2)$
$-3$	$1$	$(-3,1)$
$-6$	$2$	$(-6,2)$

Plot these points on the graph paper and join them using a straight line.
All the three lines meet at a point. $(3,-1)$