Question

Solve the system of equations: y=x+3 and y=2x+5. How did the above equations interact with each other? Write the word in BOLD that describes how the lines interacted.

a) (1,2)
b) (3,6)
c) (4,7)
d) (5,10)

Answer 1

The solution to the system of equations y = x + 3 and y = 2x + 5 is (2, 5), and the lines representing the equations intersect at the point (2, 5).

Step-by-step explanation:

The system of equations is y = x + 3 and y = 2x + 5. To solve this system, we can set the two equations equal to each other: x + 3 = 2x + 5. Now we can solve for x: x = 2. Substituting this value back into one of the original equations, we can find y: y = 2 + 3 = 5. Therefore, the solution to the system of equations is (2, 5).

The lines representing the equations

y = x + 3

and

y = 2x + 5

intersect at the point (2, 5). Therefore, the word that describes how the lines interacted is

a) (2,5).