For what values of k does the line y = kx –4 pass through the point of intersection of the lines y=2x–5 and y=–x+1?

Answer:

k = 3/2 = 1.5

Step-by-step explanation:

To find the value of k, at first we will find the point of intersection of the lines

y =2x –5 ⇒(1)

y = –x+1 ⇒ (2)

By substitution with the value of y from (1) at (2)

So, 2x - 5 = -x + 1  ⇒ Solve for x

∴ 3x = 6 ⇒ x = 6/3 = 2

By substitution with the value of x at (2)

So, y = -x + 1 = -2 + 1 = -1

So, the point of intersection of the lines is ⇒ (2,-1)

line y = kx –4 pass through the point of intersection of the lines

so, line y = kx –4 pass through the point (2,-1)

So, at x = 2 , y = -1

∴ -1 = 2k - 4 ⇒ Solve for k

∴ -1 + 4 = 2k

∴ 2k = 3

∴ k = 3/2 = 1.5

So, the value of k is 1.5

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.