1. Do Now
On your desk:
Study Guide
Whiteboard, marker, eraser

2. Do Now: Answer the following question: What can you conclude about the solution to the system of linear equations below? (Hint: It might be helpful to graph them)
𝑦=−7𝑥+1 𝑦=−7𝑥−9
They intersect at point (1, -9)
There is no intersection point and no solution
There are infinite intersection points and infinite solutions
They intersect at the point (0,-7)

3. What can you conclude about the solution to the system of linear equations below?
𝑦=5𝑥−1 1+𝑦=5𝑥
They intersect at point (0, 0)
There is no intersection point and no solution
There are infinite intersection points and infinite solutions
They intersect at the point (-1, 5)

4. Write the equations of the lines in slope-intercept form
Write the equations of the lines in slope-intercept form. What is the solution?
𝑦=− 5 3 𝑥+3 𝑦= 1 3 𝑥−3
𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛: (3,−2)

5. Tell whether the ordered pair is a solution of the given system.
(1, -2) 𝑦=7𝑥−9 𝑦=−3𝑥+1
𝑌𝐸𝑆

6. Write the equation in slope-intercept form (y=mx+b)
8𝑥−2𝑦=−18
𝑦=4𝑥+9

7. Tell whether the ordered pair is a solution of the given system.
(0,-5) 𝑦=−6𝑥+5 𝑥−𝑦=5 𝑁𝑂

8. What are the possible solutions for a system of equations?
1) ONE SOLUTION
2) NO SOLUTION
3) INFINITELY MANY SOLUTIONS

9. Solve by graphing
𝑦=3𝑥+2 𝑦=−2𝑥−3
(−1, −1)

10. Solve algebraically
𝑦=𝑥+3 𝑦=2𝑥+12
(−9, −6)

11. Solve by graphing
−2𝑥−1=𝑦 𝑥+𝑦=3
(−4, 7)

12. Solve algebraically
2𝑥+𝑦=4 3𝑥+𝑦=3
(−1, 6)

13. Write the equation in slope-intercept form (y=mx+b)
8𝑥+6𝑦=48
𝑦=− 4 3 𝑥+8

14. Tell whether the ordered pair is a solution of the given system.
(3, 6) 𝑥−𝑦=−5 2𝑥+𝑦=12
𝑌𝐸𝑆

15. Tell whether the following has one solution, no solution, or infinitely many solutions.
−6𝑥+3𝑦=3 𝑦=2𝑥+1
𝐼𝑛𝑓𝑖𝑛𝑖𝑡𝑒𝑙𝑦 𝑀𝑎𝑛𝑦 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

16. Solve algebraically
2𝑦=4𝑥+8 32𝑥+8𝑦=80
(1, 6)

17. Together Mike and Sara swam 27 laps in a pool
Together Mike and Sara swam 27 laps in a pool. Sam swam twice as many laps as Mike did. Write and solve a system of equations to determine how any laps they each swam.
Define your variables: Write a systems of equations: Solve: x=________________ y=________________