Question

draw the graph of the equation x+y=6 and 2x+3y=16 on the same graph paper. Find the coordinates of the points where the two lines intersect ​

Answer 1

Answer:

I have solve the problem. Hope it helps. Plot the points on the graph and u will get the desired graph.

Answer 2

Concept: The point that intersects the two graphs is the point that is the solution of the system of the two equations.

Given: The two equations are
x+y=6
2x+3y=16

Find: The coordinates of the points where the two lines intersect are to be determined.
And the graph of the equations is to be drawn on the same graph.

Solution:
Two draw the graph of the equations we draw tables of values
For x+y=6

x | 0 | 6
y | 6 | 0

Now join the points (0,6) and (6,0) to get the equation x+y=6 (i.e. the red line in the below-given diagram)

For 2x+3y=16

x | 8 | 0
y | 0 | $\frac{16}{3}$

Now join the points (0, $\frac{16}{3}$) and (8,0) to get the equation x+y=6 (i.e. the blue line in the below-given diagram)

We solve the system of equations to get the intersecting point
put the value of y=16-x in the next equation to get
2x+3(6-x)=16
⇒-x=16-18
⇒x=2
Putting this value in the 1st equation we get y=6-2=4

Hence, the intersecting point of the two lines is (2,4) as verified by the figure below.

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