Question

Solve the following system of linear equations graphically: $2x+y=6,x-2y+2=0$. Find the vertices of the triangle formed by the above two lines and the $x$-axis. Also find the area of the triangle.

• A. Vertices of the triangle are $A(1,2),8(5,0)$ and $C(-2,0)$ and Area: $10$ square units
• B. Vertices of the triangle are $A(4,2),8(2,0)$ and $C(-2,0)$ and Area: $15$ square units
• C. Vertices of the triangle are $A(0,2),8(1,0)$ and $C(-2,0)$ and Area: $7$ square units
• D. Vertices of the triangle are $A(2,2),8(3,0)$ and $C(-2,0)$ and Area: $5$ square units

Answer 1

The correct option is D Vertices of the triangle are $A(2,2),8(3,0)$ and $C(-2,0)$ and Area: $5$ square units

$2x+y=6$

$⟹y=6-2x$

Let, $x=1$, then $y=6-2\left(1\right)=4$

Similarly, when $x=2,y=2$

$x-2y+2=0$

$⟹x=2y-2$

Let, $y=0,$ then $x=2\left(0\right)-2=-2$

Similarly, when $y=2,x=2$

Plotting the above points on the graph, we get, the vertices of the traingle, i.e. $A(2,3),B(3,0),C(-2,0)$

$\therefore$ Area of the triangle $=\frac{1}{2}\times 5\text{units}\times 2\text{units}$

$=5$ sq. units