Question

Which of the points below is a solution to the system: y= 3x+2 and y = 5x-6

1. (3,11) 2. (2,4)
3. (4,14) 4.(18,60)

Answer 1

Let y=3x+2 be equation 1
y=5x-6 be equation 2

From 1..
x=y-2/3 (making x the subject)

Substitute the relation of x into eq2
y=5(y-2)/3-6
3y=5y-10-18 (multiplying through by the lcm,3)
3y-5y=10-18 (grouping of like-terms)
-2y=-28
y=14 (when you divide through by -2)

Putting in the value of y into the equation of x
y-2/3=x
x=14-2/3
x=12/3
x=4

Therefore the answer is 3. (4,14)

Answer 2

3. (4,14)

Explanation:

Let's test

1. (3, 11)

11 = 3(3) + 2 11 = 15 - 6

11 = 11 11 = 9

So, option 1 is wrong

2. (2,4)

4 = 6 + 2

4 = 8

So, option 2 is wrong

3. (4,14)

14 = 12 + 2 14 = 20 - 6

14 = 14 14 = 14

So, option 3 is the correct answer.