Question

Solve the following simultaneous equations graphically:

2x + 3y = 2 and x -2y =8​

Answer 1

Answer:

Consider first equation.

2x−3y+2=4x+1

3y=2x−4x+2−1

3y=−2x+1

y=(−2x+1)/3

When x=−1,

y=(−2×−1+1)/3=3/3=1

When x=2,

y=(−2×2+1)/3=−3/3=−1

When x=0.5,

y=(−2×0.5+1)/3=0

x= 0.5 ,2 ,−1

y= 0 ,−1 ,1

Mark the above points on graph. Join them.

4x+1=3x−y+2

y=3x−4x+2−1

y=−x+1

When x=0

y=0+1=1

When x=1

y=−1+1=0

When x=2

y=−2+1=−1

x= 0 ,1 ,2

y= 1 ,0 ,−1

Mark the above points on graph. Join them.

It is clear from the graph that the two lines intersect at (2,−1).

So the solution of the given equations are x=2 and y=−1.

Answer 2

Answer:

2x−3y+2=4x+1

3y=2x−4x+2−1

3y=−2x+1

y=(−2x+1)/3

When x=−1,

y=(−2×−1+1)/3=3/3=1

When x=2,

y=(−2×2+1)/3=−3/3=−1

When x=0.5,

y=(−2×0.5+1)/3=0

x= 0.5 ,2 ,−1

y= 0 ,−1 ,1

Mark the above points on graph. Join them.

4x+1=3x−y+2

y=3x−4x+2−1

y=−x+1

When x=0

y=0+1=1

When x=1

y=−1+1=0

When x=2

y=−2+1=−1

x= 0 ,1 ,2

y= 1 ,0 ,−1

Mark the above points on graph. Join them.

It is clear from the graph that the two lines intersect at (2,−1).

So the solution of the given equations are x=2 and y=−1.

solution