Question

The lines representing the pair of equations x + 3y = 6 and 2x - 3y=12 intersects at

Answer 1

Your Answer Is (6,0)

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ExplanaTion:-

Given equations:-

• ↦ x + 3y = 6.

• ↦ 2x - 3y = 12.

To Find:-

• Where the line representing these equations will intersect which means we have to find a common solution of both the equations.

So,

Lets find out the common solution by elimination method:-

So by adding both equations we get:-

↦ (x+3y) + (2x-3y) = 6 + 12.

↦ x + 3y + 2x - 3y = 18.

↦ 3x = 18.

↦ x = 18/3.

↦ x = 6.

By putting the value of x in equation 1 we get:-

↦ x + 3y = 6.

↦ 6 + 3y = 6.

↦ 3y = 0.

↦ y = 0/3.

↦ y = 0.

Therefore the required value of x and y are 6 and 0 respectively.

So point at which the line will intersect is (6,0).

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VerificaTion:-

Let usbput the values of x and y to verify the solutions:-

1)

↦ x + 3y = 6.

↦ 6 + 3(0) = 6.

↦ 6 + 0 = 6.

↦ 6 = 6.

↦ LHS = RHS,

...Hence verified...

2)

↦ 2x - 3y = 12.

↦ 2(6) - 3(0) = 12.

↦ 12 - 0 = 12.

↦ 12 = 12.

↦ LHS = RHS.

...Hence Verified...

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