Question

Find the point 3x - 7x₂ =5. of the lines x, - 5x2 = 1 and of intersection

Answer 1

Answer:

($\frac{9}{4},\frac{1}{4})$

Step-by-step explanation:

We are given that two lines

$x_1-7x_2=5$ and $x_1-5x_2=1$

We have to find the intersection point of two lines

Let $3x_1-7x_2=5$ (equation 1)

$x_1-5x_2=1$ (Equation 2)

Multiply equation 2 by 3 then subtract  from  equation 1

$-7x_2+15x_2=5-3$

$8x_2=2$

$x_2=\frac{2}{8}=\frac{1}{4}$

Substitute $x_2=\frac{1}{4}$ in the equation 1

Then, we get

$3x_1-7\frac{1}{4}=5$

$3x_1-\frac{7}{4}=5$

$3x_1=5+\frac{7}{4}=\frac{20+7}{4}=\frac{27}{4}$

$x_1=\frac{27}{4\times 3}=\frac{9}{4}$

Hence, the intersection point of two given lines is ($\frac{9}{4},\frac{1}{4})$