Question

Find the point (x1,x2) that lies on the line x1 +5x2 =7 and on the line x1 - 2x2 = -2.

Answer 1

Given :

Two equation $x_1 +5x_2 =7$ and $x_1 - 2x_2 = -2$ .

To Find :

The point of intersection of these lines .

Solution :

We will use elimination method :

From equation 1 :

$x_1=7-5x_2$

Putting value of $x_1$ in equation 2 we get :

$(7-5x_2)-2x_2=-2\\\\7-7x_2=-2\\\\x_2=\dfrac{9}{7}$

Putting value of $x_2$ in equation 1 we get :

$x_1+5\times \dfrac{9}{7}=7\\\\x_1=\dfrac{4}{7}$

Therefore , point of interaction is $(\dfrac{4}{7},\dfrac{9}{7})$ .

Hence , this is the required solution .