Can you explain the answer of this question below:The area of the triangle formed by the lines 2x + y = 6, 2x – y + 2 = 0 and the x – axis isA:15sq. unitsB:8sq. unitsC:10sq. unitsD:12sq. unitsThe answer is b.

Question

Can you explain the answer of this question below:The area of the triangle formed by the lines 2x + y = 6, 2x &#8211; y + 2 = 0 and the x &#8211; axis isA:15sq. unitsB:8sq. unitsC:10sq. unitsD:12sq. unitsThe answer is b.

Answer

Explanation:

Solving the three equations 2x+y=6, 2x-y+2=0 and x=0 (equation of x-axis)

we get the three vertices of the triangle to be (1,4); (3,0) and (-1,0)

Therefore area of the triangle is,

=1/2 [1 (0 - 0) + {-1 (0 - 4)} + 3 (4 - 0)]

= 1/2 x 16 = 8

You can know about Important Definitions & Formulas: Pair of Linear Equations in Two Variables through the document:

Important Definitions & Formulas: Pair of Linear Equations in Two Variables

https://edurev.in/studytube/important-definitions-formulas-pair-of-linear-equa/7c4df278-2926-42af-b2c4-82cee157f6cd_t

Answer

Here are the two solutions of each of the given equations. 2x+y = 6
2x+y=0

The area bounded by the given lines and x−axis has been shaded in the graph.
∴

Answer

Here are the two solutions of each of the given equations. 2x+y = 6
2x+y=0

The area bounded by the given lines and x−axis has been shaded in the graph.
∴

Answer

To find the area of the triangle formed by the lines, we first need to find the vertices of the triangle.

The lines 2x + y = 6 and 2x - y = 2 can be rewritten in slope-intercept form:

2x + y = 6
y = -2x + 6

2x - y = 2
y = 2x - 2

Now we can find the points where these lines intersect.

Substitute the equation y = -2x + 6 into the equation y = 2x - 2:

-2x + 6 = 2x - 2

Add 2x to both sides:

6 = 4x - 2

Add 2 to both sides:

8 = 4x

Divide by 4:

x = 2

Substitute this value of x back into the equation y = -2x + 6:

y = -2(2) + 6
y = -4 + 6
y = 2

So the first intersection point is (2, 2).

Now substitute the equation y = 2x - 2 into the equation y = -2x + 6:

2x - 2 = -2x + 6

Add 2x to both sides:

4x - 2 = 6

Add 2 to both sides:

4x = 8

Divide by 4:

x = 2

Substitute this value of x back into the equation y = 2x - 2:

y = 2(2) - 2
y = 4 - 2
y = 2

So the second intersection point is also (2, 2).

The third vertex of the triangle is the point where the lines 2x + y = 6 and 2x - y = 2 intersect.

Subtract the equation 2x - y = 2 from the equation 2x + y = 6:

2x + y - (2x - y) = 6 - 2

Simplify:

2x + y - 2x + y = 4

Combine like terms:

2y = 4

Divide by 2:

y = 2

Substitute this value of y back into the equation 2x + y = 6:

2x + 2 = 6

Subtract 2 from both sides:

2x = 4

Divide by 2:

x = 2

So the third intersection point is (2, 2).

Now we can find the area of the triangle using the formula:

Area = 1/2 * base * height

The base of the triangle is the distance between the intersection points (2, 2) and (2, 2), which is 0. Therefore, the base is 0.

The height of the triangle is the distance between the point (2, 2) and the line 2x + y = 6. To find this distance, we can use the formula for the distance between a point and a line:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

In this case, A = 2, B = 1, C = -6, and the point (x, y) = (2

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