SWBAT: Graph the Systems of Equations

SWBAT: Graph the Systems of Equations

Step 1: Calculate the Midpoint.

𝒎𝒊𝒅 = (𝟏𝟎 + 𝟒

𝟐,

−𝟗 + −𝟓

𝟐)

𝒎𝒊𝒅 = (𝟕, −𝟕)

Step 2: Calculate the radius of the circle.

ΔX ΔY

r2 = ∆𝒙 𝟐+ ∆𝒚 𝟐

10-4 -6

-9-(-5) -4

r2 = −𝟔 𝟐+ −𝟒 𝟐

r2 = 𝟓𝟐

(x - 7)2 + (y + 7)2 = 52

SWBAT: Graph the Systems of Equations

(2,3)

3 2

SWBAT: Graph the Systems of Equations

A quadratic-linear system consists of a quadratic equation and a linear equation. The solution of a quadratic-linear system is the set of ordered pairs of numbers that make both equations true. As shown below, the line may intersect the curve in two, one, or no points. Thus the solution set may contain two ordered pairs, one ordered pair, or no ordered pairs.

Example #1:

SWBAT: Graph the Systems of Equations

Example #2:

SWBAT: Graph the Systems of Equations

#1) Quadratic Linear System of Equations

SWBAT: Graph the Systems of Equations

Vertex = (2,-1)

2 -1

3

1

4

5 6

0

-1 -2

0

3

8 15

0

3

8

15

1

3

Rule: 𝟏𝒂

𝟏,

𝟑𝒂

𝟏,

𝟓𝒂

𝟏,

𝟕𝒂

𝟏,

𝟗𝒂

𝟏

-4

1

𝟒

𝟐 = 𝟐

−𝟏

Quadratic Linear System of Equations:

SWBAT: Graph the Systems of Equations

Rule: 𝟏𝒂

𝟏,

𝟑𝒂

𝟏,

𝟓𝒂

𝟏,

𝟕𝒂

𝟏,

𝟗𝒂

𝟏

𝟏

𝟏,𝟑

𝟏,𝟓

𝟏,𝟕

𝟏,𝟗

𝟏

#2) Quadratic Linear System of Equations:

SWBAT: Graph the Systems of Equations

Vertex = ( , )

x + y = 4

Rule: 𝟏𝒂

𝟏,

𝟑𝒂

𝟏,

𝟓𝒂

𝟏,

𝟕𝒂

𝟏,

𝟗𝒂

𝟏

#2) Quadratic Linear System of Equations:

SWBAT: Graph the Systems of Equations

1 5

2

0

3

4 5

-1

-2 -3

4

1

-4 -11

4

1

-4

-11

-1

4 Vertex = (1,5)

Rule: 𝟏𝒂

𝟏,

𝟑𝒂

𝟏,

𝟓𝒂

𝟏,

𝟕𝒂

𝟏,

𝟗𝒂

𝟏

x + y = 4

Rule: −𝟏

𝟏,

−𝟑

𝟏,

−𝟓

𝟏,

−𝟕

𝟏,

−𝟗

𝟏

#2) Quadratic Linear System of Equations

SWBAT: Graph the Systems of Equations

SWBAT: Graph the Systems of Equations

y = x

c: (0,0); r = 𝟒 = 𝟐

; m=𝟏

𝟏 ; b = 𝟎

2

SWBAT: Solve a Non-Linear System of Equations

𝑥2 + 𝑦2 = 4 𝑦 = 𝑥

Step 1: Substitute “y” with “x”

𝑥2 + (𝑥)2= 4

Step 2: Solve for x

𝑥2 + 𝑥2 = 4

2𝑥2 = 4 2 2

𝑥2 = 2

𝑥2 = 2

𝑥 = ± 2

Step 3: Find y for each x.

𝑦 = 𝑥 𝑊ℎ𝑒𝑛 𝑥 = 2

y = 2 𝑊ℎ𝑒𝑛 𝑥 = − 2

y = - 2

Solutions = ( 2, 2) and (− 2,− 2)

SWBAT: Graph the Systems of Equations

Solutions = ( 2, 2) and (− 2,− 2)

Solutions (𝟏. 𝟒, 1.4) and (−1.4,−1.4)

SWBAT: Graph the Systems of Equations

𝐹𝑖𝑟𝑠𝑡 𝑐𝑖𝑟𝑐𝑙𝑒: (𝑥 − 3)2+ (𝑦 − 5)2= 25

c: (3,5); r = 𝟐𝟓 = 𝟓

𝑆𝑒𝑐𝑜𝑛𝑑 𝑐𝑖𝑟𝑐𝑙𝑒: (𝑥 − 7)2+ (𝑦 − 5)2= 9

c: (7,5); r = 𝟗 = 𝟑

Solutions = (𝟕, 𝟖) and (7,2)

SWBAT: Graph the Systems of Equations

SWBAT: Graph the Systems of Equations