Question

Solve the equations graphically:

2x + y = 2; 2y – x = 4

What is the area of the triangle formed by the two lines and the line y = 0?​

Answer 1

Step-by-step explanation:

Area of triangle is 5 square unit.

Step-by-step explanation:

Given : Equation 1 - 2x+y=22x+y=2

Equation 2 - 2y-x=42y−x=4

Equation 3- y=0y=0

Solve the equation graphically and find the area of the triangle formed.

Solution : The solution graphically is attached in which equation 1,2 and 3 form the triangle by points (0,2),(-4,0),(1,0) and shaded region represent the triangle formed.

Now, to find area of triangle we need base and height.

From graphically we see that the height of triangle is (0,2)=2 unit and base is (1-(-4))=5 unit.

Area of triangle A= \frac{1}{2}\times b\times hA=

2

1

×b×h

where b is the base and h is the height,

A= \frac{1}{2}\times 5\times 2= 5 unit^2A=

2

1

×5×2=5unit

2

Therefore, Area of triangle is 5 square unit.

Answer 2

X=1

y 0

Explanation:

Given that two equations-

-----(1)

2x- y 2

4x - y= 4

--(2)

Slope intercept form is y = mx + b

where m is slope & bis y intercept

Solve equation 1 for y:

y 2x-2

y intercept is = -2; So, coordinate is = (0.

2)

Now find the x-intercept. In order to find

the x-intercept we put y = O in given

equation.

O 2x 2

X1

So, coordinate is = (1,0)

Graph this line.

Solve equation 2 for y:

y 4x 4

y 4x-4

y intercept is = -4; So, coordinate is = (0.

-4)

Now find the x-intercept. In order to find

the x-intercept we put y = 0 in given

equation.

O 4x-4

X =1

So, coordinate is = (1,0)

Graph the line.

We see that both the lines intersect at

(1,0).

So, solution set is (1,0)

x= 1

y 0