Do Now On your desk: Study Guide Whiteboard, marker, eraser
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)
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)
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)
Tell whether the ordered pair is a solution of the given system. (1, -2) 𝑦=7𝑥−9 𝑦=−3𝑥+1 𝑌𝐸𝑆
Write the equation in slope-intercept form (y=mx+b) 8𝑥−2𝑦=−18 𝑦=4𝑥+9
Tell whether the ordered pair is a solution of the given system. (0,-5) 𝑦=−6𝑥+5 𝑥−𝑦=5 𝑁𝑂
What are the possible solutions for a system of equations? 1) ONE SOLUTION 2) NO SOLUTION 3) INFINITELY MANY SOLUTIONS
Solve by graphing 𝑦=3𝑥+2 𝑦=−2𝑥−3 (−1, −1)
Solve algebraically 𝑦=𝑥+3 𝑦=2𝑥+12 (−9, −6)
Solve by graphing −2𝑥−1=𝑦 𝑥+𝑦=3 (−4, 7)
Solve algebraically 2𝑥+𝑦=4 3𝑥+𝑦=3 (−1, 6)
Write the equation in slope-intercept form (y=mx+b) 8𝑥+6𝑦=48 𝑦=− 4 3 𝑥+8
Tell whether the ordered pair is a solution of the given system. (3, 6) 𝑥−𝑦=−5 2𝑥+𝑦=12 𝑌𝐸𝑆
Tell whether the following has one solution, no solution, or infinitely many solutions. −6𝑥+3𝑦=3 𝑦=2𝑥+1 𝐼𝑛𝑓𝑖𝑛𝑖𝑡𝑒𝑙𝑦 𝑀𝑎𝑛𝑦 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠
Solve algebraically 2𝑦=4𝑥+8 32𝑥+8𝑦=80 (1, 6)
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=________________