AgendaLesson 6-1 – Solving Systems by Graphing

Standards9.0 Solve a system of two linear equations in two variables and

interpret the answer graphically

Warm UpReview

Notes – Graphing systemsPracticeReview

Homework – Page 576 problems 1 to 3 all

Warm Up

Write the equation in point-slope form for the line that passes through the given points

a. (2, 1) and (4, 4)

b. (0, 0) and (2, 4)

c. (1, 5) and (2, 3)

Homework – Page 576 problems 1 to 3 all

Systems

System of linear equations– two or more linear equations considered together

Solution of a system of linear equations– the ordered pair that satisfies each of the equations in the system.

Solving a system of equationsEXAMPLE 1

Solve by graphing: y = 2x – 3 y = x – 1

Plot first y-intercept

Use slope to plot 2nd point

Connect the points

Plot second y-intercept

Use slope to plot 2nd point

Connect the points

ApplicationsEXAMPLE 2

The system and graph below represent the growth pattern for 2 plants

H(d) = 4d + 6H(d) = 2d + 10

0 1 2 3 4 5 6 7 8 9

4

8

12

16

Hei

ght

in c

m

Number of days

Interpreting SolutionsEXAMPLE 3

Part 1 find the solution by graphing for:H(d) = 4d + 6H(d) = 2d + 10

The lines intersect at (2, 14)

Part 2 Interpret the solution

At 2 days, both plants will be the same height, 14 cm tall

0 1 2 3 4 5 6 7 8 9

4

8

12

16

Hei

ght

in c

m

Number of days

Systems with no solutionsEXAMPLE 4

No solution for linear systems means the lines are parallel and do not intersect.

y = x – 1y = x + 2

Systems with infinitely Many SolutionsEXAMPLE 5

Systems with infinitely many solutions is a system where the lines are the same line

y = 2x + 64x – 2y = –12

Class work – Please do these nowPage 279 problems 2 to 22 even

Homework – Please do at home tonight Page 576 problems 1 to 3 all