Determine the value of k such that the following system of linear equations has a solution, and then find the solution.

Question

Determine the value of k such that the following system of linear equations has a solution, and then find the solution.
2x + 3y = 5
x + 4y = 10
5x + ky = 11

k = ???

(x,y) ?? 

Answer 1

Hi Sydney,

 

Since you have an unknown value "k" you can use substitution to solve for (x, y) using the first two equations. Then plug these into the third equation and solve for k.

 

 

2x + 3y = 5

x + 4y = 10 

x = 10 - 4y  (substitute this in for x)

 

2(10 - 4y) + 3y = 5

20 - 8y + 3y = 5

 

combine like terms

 

15 = 5y

 

y = 3

 

x + 4(3) = 10

x + 12 = 10

 

x = -2

 

So the first two lines intersect at the point (-2, 3)

 

Use this point in the third equation to find the k value that makes this line also intersect at that same point.

 

5x + ky = 11

 

5(-2) + 3k = 11

-10 + 3k = 11

3k = 21

 

k = 7