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{ = -}(3)/(4)\text{x +}(25)/(4)`

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

`2x-2\text{ = -}(3)/(4)\text{x +}(25)/(4)`

this is equivalent to:

`2x\text{ + }(3)/(4)x\text{ = }(25)/(4)+2`

this is equivalent to:

`(11)/(4)x\text{ = }(33)/(4)`

this is equivalent to:

`11x\text{ = 33}`

this is equivalent to:

`x\text{ = }(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}`