Question

Determine, graphically whether the system of equations x – 2y = 2, 4x – 2y = 5 is consistent or in-consistent.

Answer 1

Equations are consistent x – 2y = 2, 4x – 2y = 5

Step-by-step explanation:

x x - 2y =  2 4x - 2y = 5

x        y                   y

-4 -3                -10.5

-3 -2.5               -8.5

-2 -2               -6.5

-1 -1.5               -4.5

0 -1               -2.5

1 -0.5       -0.5

2 0               1.5

3 0.5               3.5

4 1               5.5

Both equation intersect at (1  , -0.5)

hence Equations are consistent

equations is called as consistent if there is at least one set of values for the unknowns that satisfies each equation in the system

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Answer 2

Answer:

Step-by-step explanation:

x – 2y = 2……. (i)

4x – 2y = 5……. (ii)

For equation (i),

⇒ y = (x – 2)/2

When x = 2, we have y = (2 – 2)/2 = 0

When x = 0, we have y = (0 – 2)/2 = -1

For equation (ii),

We solve for x:

⇒ x = (5 + 2y)/4

So, when y = 0

x = (5 + 2(0))/4 = 5/4

And, when y = 1.5

⇒ x = (5 + 2(1))/4 = 7/4

Graph of the equations (i) and (ii) is as below:

It is clearly seen that the two lines intersect at (1,0)

Hence, the system of equations is consistent.