Essential Question:What does the graph of an independent system of linear equations in two variables look like?

Get both lines into slope-intercept form y = mx + b Get “y” by itself

Graph each line Plot y-intercept (“b”) on the y-axis Use the slope (“m” – rise over run) to make

a second point Connect the two points

Solution is where the two lines intersect

Solve by graphing 2x + y = 5 -x + y = 2

Solve both equations for y

Graph both lines on the same grid

Intersection is the solution

y = -2x + 5y = x + 2

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

solution: (1, 3)

What does that point (1, 3) mean? It means that x = 1 and y = 3 is a

solution to both equations.▪ 2x + y = 5

2(1) + (3) = 52 + 3 = 5▪ -x + y = 2

-(1) + (3) = 2-1 + 3 = 2

Independent System – 1 solution Intersecting Lines Lines have different slopes

Inconsistent System – No solution Parallel Lines Lines have same slope & different y-

intercepts Dependent System – Infinite solutions

Same line Lines have same slope & same y-intercept

Classify the system without graphing y = 2x + 3 -2x + y = 1

Solve both equations for y

Do the graphs have the same slope? Yes? See next question No?

Independent Are they the same line?▪ Yes? Dependent No? Inconsistent

y = 2x + 3 y = 2x + 1

Classify the system without graphing y = 2x + 3 -4x + 2y = 6

Solve both equations for y

Do the graphs have the same slope? Yes? See next question No?

Independent Are they the same line?▪ Yes? Dependent No? Inconsistent

y = 2x + 3 y = 2x + 3

Assignment Page 120 – 121 1 – 7 & 13 – 23, odd problems Show work (e.g. converting equations)