Question

Q-6. Solve the following system of linear equations graphically: 2x - y = 4, x - y = 1​

Answer 1

Step-by-step explanation:

2x−y−4=0 …(i)

y=2x−4

When x=1,y=2×1−4=2−4=−2

When x=2,y=2×2−4=4−4=0

When x=3,y=2×3−4=6−4=2

x= 1 ,2 ,3

y= −2 ,0 ,2

Mark the above points on graph. Join them.

x+y+1=0 …(ii)

y=−x−1

When x=0,y=0−1=−1

When x=−2,y=2−1=1

When x=−1,y=1−1=0

x= −2 ,−1 ,0

y= 1 ,0 ,−1

Mark the above points on graph. Join them.

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

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

The area of the triangle formed by these lines and Y axis =1/2 ×base×height

=1/2×3×1

=1.5sq. units

Hence area of the triangle is 1.5sq. units.

Answer 2

Answer:

x=3 and y=4

Step-by-step explanation:

$\\ \sf\hookrightarrow 2x-y=4-----(1)$

$\\ \sf\hookrightarrow x-y=1------(2)$

• By subtracting eq(2) from eq(1) we get

$\\ \bf\hookrightarrow x=3$

• Substitute the value of x in eq(2)

$\\ \sf\hookrightarrow 3-y=1$

$\\ \sf\hookrightarrow y=1+3$

$\\ \bf\hookrightarrow y=4$