Question

Find the point of intersection of lines given
y=2x+1
y=-x+11

Answer 1

Answer: (10/3, 23/3)

Explanation:

To determine the point of intersection of the two lines, we would solve both equations simultaneously. The given system of linear equations is expressed as

y = 2x + 1- - - - - - - - - - - - -1

y = - x + 11 - - - - - - - - - - - -2

We would eliminate y by

Subtracting equation 2 from equation 1, it becomes

0 = 3x - 10

Adding 10 to the left hand side and the right hand of the equation, it becomes

3x - 10 + 10 = 0 + 10

3x = 10

Dividing the left hand side and the right hand side of the equation by 3, it becomes

3x/3 = 10/3

x = 10/3

Substituting

x = 10/3 into equation 1, it becomes

y = 2 × 10/3 + 1

y = 20/3 + 1

y = 23/3

Answer 2

(10, 21)

Explanation:

To get the point of intersection of the lines given ( it means we need to find at what value of x will correspond to the value of y)

y = 2x+1

y = x+11

insert equation i in equation ii

2x+1=x+11

2x-x = 11-1

x = 10

y = 2x+1 = 2(10)+1 = 20+1 = 21

(x,y) = (10, 21)