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MATHMAA

# Linear Equation Two Variable

In Linear Equation Two Variable , we have to find unknown values of given condition.

Level 1

1. Find the value of 'a' so that the point (3,a) lies on the line represented   by  2x - 3y = 5.

Solution:-

As the point (3, a) lies on the line 2x - 3y = 5 ,Then we can say that the give point is a solution of that line .

Hence substitute x = 3 and y = a .

2x - 3y = 5

2(3) - 3(a) = 5

6 - 3a = 5

3a = 1

a = 1/3 .

Therefore, a = 1/3.

2. Find the value of 'k' so that the lines 2x - 3y = 9 and kx - 9y = 18 will be parallel.

Solution:-

If  $$a_{1}x + b_{1}y + c_1 = 0$$ and $$a_{2}x + b_{2}y + c_2 = 0$$ are parallel lines then,

$$\frac {a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$

Hence, If 2x - 3y = 9 and kx - 9y = 18 are parallel lines then ,

$$\frac {2}{k} = \frac{-3}{-9} \neq \frac{9}{18}$$
$$\frac {2}{k} = \frac{3}{9}$$

2*9 = 3*k

k = 6

Therefore, k = 6.

3. Find the value of 'k' for which x + 2y = 5 and 3x + ky + 15 = 0 is inconsistent.

Solution:-

If  $$a_{1}x + b_{1}y + c_1 = 0$$ and $$a_{2}x + b_{2}y + c_2 = 0$$ are inconsistent then,

$$\frac {a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$$

Hence, If x + 2y = 5 and 3x + ky = -15 are inconsistent then ,

$$\frac {1}{3} = \frac{2}{k} \neq \frac{5}{-15}$$

$$\frac {1}{3} = \frac{2}{k}$$

1*k = 3*2

k = 6

Therefore, k = 6.

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