Standard 9

Solve a system of two linear equations

x = 7

x +

2x = 14

Example One.Instructions:Use substitution. Solve for x

2x+ 4 = 18-4 -4

÷2 ÷2

= 18 is x + 4 x + 4

x = 7

x +

2x = 14

Example One.Instructions:Use substitution. Solve for x

2x+ 4 = 18-4 -4

÷2 ÷2

= 18 y = x + 4 x + 4 y

y = x + 4

y = ( ) + 4y = 11(7,11)

x = 77

x = 5

x + 2

3x = 15

Example Two.Instructions:Use substitution. Solve for x

3x+ 6 = 21-6 -6

÷3 ÷3

= 21 is x + 3

x+ 2x + 6 = 21

(x + 3)

a +3

2 a2 6

3x = 3

2x + 2

4x = 12

Example Three.Instructions:

x + 4

4x+ 8 = 20-8 -8

÷4 ÷4y = x + 4

y = ( ) + 4y = 7(3,7)

yy = 20 = x + 4 y =( )

2x+ 2x + 8 = 20

y - x = 4 +x +x

n3n910n12

n1210n12 -12n -12n

010

)nn3(310n3n9 3

3n +n9n +3n

False

)nn3(3y 10n3n9y

Parallel lines

and

16a416a4 -16 -16

a4a4 -4a -4a

00

)4a(4a316a7 4

a +44a +16

True

)4a(4y a316a7y

Infinite many solutions

Instructions: Use substitution to solve for xClasswork One

+ 3x = 6 (1)is 2x + 1

+ 5x = 2 (2) is 3x - 14

+ 3x = 11 (2) is x + 3

+ 3x = 18 (4) is x + 2

Instructions: Find where the lines intersect.Classwork Two

(x,y)y + 3x = 6 (1,3)y = 2x + 1

y + 5x = 2 (2,-8)y = 3x - 14

2y + 3x = 11 (1,4)y = x + 3

3y + 3x = 18 (2,4)y = x + 2

Instructions: Find where the lines intersect.Classwork Three

(x,y)y + 2x = 9 (2,5)y – 2x = 1

y + 4x = 7 (3,-5)y + 3x = 4

2y + 3x = 14 (2,4)y – x = 2

2y + 3x = 8 (4,-2)y + x = 2

Find the value of n that makes the equation trueIf no value of n works show thatIf all values of n work show that

3) 8(n 3) - 9(n

7) 3(-b 3) - (2b-

6n3)2n(3

3)2n(59n24n3

10n7)1n(4)2n(3

6) 3(-5b 3) - 4(4b- 3) 4(4n 4) 3(5n

8) 5(11n 7) 9(6n

5) 2(n 5 2n

9n33n5

n2n3n10n4

n714n6

92n5n9 18n4n3

2) (3m 5) 4(-m-

Standard 14 solve quadratic equations

ax² + bx + c = 0