Question

the coordinates of the points of intersection of the lines 2x+3y 5 5x 8y 13 ​

Answer 1

Answer:

answer in the attachment

Answer 2

Given,

Equations of two lines,

2x + 3y = 5,

5x + 8y = 13.

To find,

Coordinates of point of intersection.

Solution,

When the equations for two lines are given, their point of intersection can be found simply by solving the equations for the variables, and the value of x- and y-coordinates will be the intersection point.

So, here the equations are,

2x + 3y = 5     ...(1)

5x + 8y = 13     ...(2)

Solving these by elimination method.

First, multiply eq. (1) by 5, and eq. (2) by 2, so as to make the coefficients of x equal.

We get new equations,

10x + 15y = 25     ...(3)

10x + 16y = 26     ...(4)

Now subtracting eq. (3) from (4), we get,

(10x + 16y) - (10x + 15y) = 26 - 25

⇒ 10x + 16y - 10x - 15y = 26 - 25

⇒ y = 1.

Substituting this value in (1), we get,

2x + 3·(1) = 5

⇒ 2x = 5 - 3

⇒ 2x = 2

⇒ x = 1.

So, we can see that the x- and y-coordinates are x = 1, y = 1.

Therefore, the coordinates of the point of intersection of the given lines will be (1, 1).