Practice: Systems of Equations

1. Is (3, 5) a solution to: y = 2x - 1 and y = x + 2?

Equation 1: 5 = 2(3) - 1 = _____ | Equation 2: 5 = 3 + 2 = _____

Answer: YES / NO

2. Is (4, -2) a solution to: x + y = 2 and 2x - y = 10?

Equation 1: _____________ | Equation 2: _____________

Answer: YES / NO

3. Is (1, 4) a solution to: y = 3x + 1 and 2x + y = 5?

Equation 1: _____________ | Equation 2: _____________

Answer: YES / NO

4. y = x + 3 and 2x + y = 12

Solution: ( , )

5. y = 2x - 5 and x + y = 4

Solution: ( , )

6. x = 3y and 2x + y = 14

Solution: ( , )

7. y = -x + 8 and 3x + y = 12

Solution: ( , )

8. y = 3x + 2 and y = 3x - 4

Slopes: _____ and _____ | Y-intercepts: _____ and _____

Number of solutions: _____________ (One / None / Infinite)

9. y = 2x + 1 and y = -x + 4

Slopes: _____ and _____ | Different slopes?

Number of solutions: _____________ (One / None / Infinite)

10. y = 4x - 3 and 2y = 8x - 6

(Hint: Rewrite the second equation in y = mx + b form first)

Second equation simplified: y = _____________

Number of solutions: _____________ (One / None / Infinite)

11. Movie Theater A charges $12 per ticket. Theater B charges $8 per ticket plus a $20 membership fee. For how many tickets will the total cost be the same?

Let x = number of tickets, y = total cost

Theater A equation: y = _____________

Theater B equation: y = _____________

Answer: _______ tickets (cost will be $_______ at each theater)

12. The sum of two numbers is 20. One number is 4 more than the other. Find the two numbers.

Let x = one number, y = other number

Equation 1 (sum): _____________

Equation 2 (relationship): _____________

The two numbers are: _______ and _______

13. A phone plan costs $30 per month plus $0.05 per text. Another plan costs $20 per month plus $0.10 per text. After how many texts will the costs be equal?

Let x = number of texts, y = monthly cost

Plan 1: y = _____________ | Plan 2: y = _____________

Answer: _______ texts (cost will be $_______)