# Calculate the intercepting point of the lines x+7y=21 and 2x-y=11

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### 4 Answers

x + 7y = 21......(1)

2x - y = 11.........(2)

The intercepting point is the solution for the system.

We wil use the elimination method to solve:

Multiply (2) by 7 and add to (1):

==> 15x = 98

==> divide by 15:

==> x= 98/15

To find y, we will substiute in (2):

y= 2x - 11

y= 2(98/15) - 11

= 196/15 - 11

= (196- 165)/15= 31/15

==> y= 31/15

Then the intercepting point is:

**P ( 98/15, 31/15)**

Let's express the two lines as:

x+7y=21

=> x= 21 - 7y

and

2x-y=11

=> x= (11 + y) / 2

Now at the point of intersection the value of x and y is the same for both the lines. So we equate 21 - 7y and (11 + y) / 2

This gives:

21 - 7y = (11 + y) / 2

=> 42 - 14y = 11 +y

=> 42 - 11 = y + 14y

=> 15 y = 31

=> y = 31/ 15

Now substitute y = 31/ 15 in 2x-y=11

=> 2x - 31/15 = 11

=> 2x = 11 + 31/15

=> 2x = 196/ 15

=> x = 98/ 15

**Therefore the point of interception is ( 98/ 15, 31/15)**

x+7y = 21.........(1)

2x-y = 11..........(2)

FRom (1), x = 21-7y. Substituting this value of x in eq (2), we get:

2(21-7y) -y = 11. Simplify the left:

42-14y -y = 11.

-15y = 11-42 = -31.

**y **= -31/-15 = **31/15.**

Substituting this value in (1), we get:

x+7(31/15) = 21

**x** = 11-7(31/15) = **98/15**

To determine the intercepting point of the lines, we'll have to solve the system formed form the equations of the lines.

x+7y=21 (1)

2x-y=11 (2)

The solution of this system represents the coordinates of the intercepting point.

We'll solve the system using elimination method. For this reason, we'll multiply (2) by 7:

14x - 7y = 77 (3)

We'll add (3) to (1):

14x - 7y + x+7y = 77 + 21

We'll eliminate like terms:

15x = 98

We'll divide by 15:

**x = 98/15**

We'll susbtitute x in (1) and we'll gte:

98/15 + 7y=21

We'll subtract 98/15 both sides:

7y = 21 - 98/15

7y = (21*15-98)/15

We'll divide by 7:

**y = 217/105**

**The coordinates of the intercepting point are: (98/15 , 217/105).**