Question

The equations of 2 lines are shown below. 2x - y = 2 3x + 4y = 25 What is the product of (x.y) of the point of intersection?

Answer 1

Question:

The equations of 2 lines are shown below. 2x - y = 2 3x + 4y = 25 What is the product of (x.y) of the point of intersection?​

Solution:

Consider the following line equations:

Equation 1

$2x-y\text{ = 2}$

Equation 2:

$3x+4y\text{ = 2}5$

Now, solving equation 1 and equation 2 for the variable y, we get:

Equation 3:

$y\text{ = 2x-2}$

and

Equation 4:

$y\text{ = -}\frac{3}{4}\text{x +}\frac{25}{4}$

now, if we relate equations 3 and 4 we obtain:

$2x-2\text{ = -}\frac{3}{4}\text{x +}\frac{25}{4}$

this is equivalent to:

$2x\text{ + }\frac{3}{4}x\text{ = }\frac{25}{4}+2$

this is equivalent to:

$\frac{11}{4}x\text{ = }\frac{33}{4}$

this is equivalent to:

$11x\text{ = 33}$

this is equivalent to:

$x\text{ = }\frac{33}{11}=\text{ 3}$

then:

$x\text{ = 3}$

now, replacing this in equation 3, we get:

$y\text{ = 2(3)-2 = 6-2 = 4}$

thus

$y\text{ = 4}$

Thus the point of the intersection is (x,y) = (3,4) and we can conclude that the product of x = 3 and y = 4 is :

$x\text{ . y = 3 . 4 = 12}$