Question

Solve the following system.
y = x + 3
2x + y = 9

(2, 5)

(5, 2)

(−2, 5)

(2, −5)

Answer 1

substitute x+3 from the first equation in for y in the second equation and solve.
2x+(x+3)=9
3x+3=9
3x=6
x=2

Use this value of x to solve for y in the first equation.
y=2+3
y=5
Answer is (2,5)

Answer 2

Which set of equations would be used to solve this word problem?

An airplane flew 3 hours with a 30 mph head wind. The return trip with a tail wind of the same speed took 2 hours. Find the speed of the plane in still air.

d = 3(r − 30) and d = 2(r + 30)

d = 3(r + 30) and d = 2(r − 30)

d = 5(r + 30)

None of these systems can be used to solve this problem.

Answer 3

[6.06] Which point lies in the solution set for the following system of inequalities?

2x + y < 4
x − y > 3

(2, −3)

(3, 4)

(5, −2)

(0, 0)

Answer 4

The graph of the following system of equations is
−2x + y = 3
−4x + 2y = 6

Overlapping lines

Parallel lines

Intersecting lines

Answer 5

Part 1:
For the following system of equations, write your own real world scenario that describes what is happening. Use complete sentences and correct grammar in your scenario.

Part 2:
Solve the system and explain what the results mean according to your scenario.

2x + y = 11
3x + 4y = 24