Question

Draw the graphs of the equations 3x – 2y = 4 and x+y-3 = 0.
On the same graph paper, find the coordinates of the point where the two graph lines intersect.​

Answer 1

It is given

3x−2y=4

We can also write it as

2y=3x−4

$\bold{y = \frac{3x - 4}{2} }$

Substituting x=2 in the given equation

$\bold{y = \frac{3(2) - 4}{2} }$

So we get

$\bold{y = \frac{6 -4 }{2} }$

$\bold{y = \frac{2}{2} }$

By division

y=1

Substituting x=−2 in the given equation

$\bold{y = \frac{3( - 2) - 4}{2} }$

So we get

$\bold{y = \frac{ - 6 - 4}{2} }$

$\bold{y = \frac{ - 10}{2} }$

By division

y=−5

x 2 -2

y 1 -5

Now draw a graph using the points A(2,1) and B(-2,-5)

Join the points AB through a line and extend in both the directions

It is given

x+y−3=0

We can also write it as

y=3−x

Substituting x=1 in the given equation

y=3−1 So we get

y=2

Substituting x=−1 in the given equation

y=3−(−1)

So we get

y=4

x 1 -1

y 2 4

Now draw a graph using the points C(1,2) and D(−1,4)

Join the points CD through a line and extend in both the directions.

Therefore the coordinates of the point where the two graph lines intersect is A(2,1)

Answer 2

Step-by-step explanation:

see the attachment for answers