Question

Determine the point of intersection between the lines with equations x+3y=5 and 3x−2y=26.

Answer 1

Answer:

(8,-1)

Step-by-step explanation:

The point of intersection can be found out by solving the system of equations.

1. x + 3y = 5
2. 3x - 2y = 26

Multiply (1) by 3 :-

→ 3 ( x + 3y ) = 5 × 3

→ 3x + 9y = 15

Subtracting 3(1) and 2 :-

→ 3x + 9y - 3x +2y = 15 - 26

→ 11y = -11

→ y = (-1)

Put it in 1 :-

→ x -3 = 5

→ x = 3 + 5

→ x = 8

Hence the point of intersection is (8,-1)

Answer 2

Answer:

the ans is :

Step-by-step explanation:

First, it would be helpful to draw a quick sketch of the lines. It helps to visualize the problem.

To find the intersection point, we need to find the point where x and y are the same value in both equations.

The line equations:

6x+2y=26 ................... 1

2x+3y=18 ................... 2

Can be rearranged to the common line equation form: y = mx + c

y = 13 - 3x ................... 3

y = 6 - 2/3 x ................. 4

At the intersection point, y will be equal for both equations. So, we can set 3 equal to 4 and solve for x.

13- 3x = 6 - 2/3 x

13 = 6 + 3x - 2/3x ....... add 3x to both sides

13 = 6 + 2 1/3x ........ simplify

7 = 2 1/3 x ........ subtract 13 from both sides

7 = 7/3 x ......... multiply both sides by 3/7

3 = x

To calculate the y-coordinate substitute x = 3 into 3.

y = 13 - 3x

y = 13 - 3(3)

y = 4

To check your answer, substitute the values for x and y into the other equation, 4.

The point of intersection is (3,4).

If you drew a sketch of the problem, you should be able to see that this point of intersection makes sense.