Pre Calculus Systems of Equations

Substitution

100

2x+y=15

y=3+x

x=4

y=7

200

x+4y=13

2x-3y=4

x=5

y=2

300

x-2y+4z=15

5y-2z=2

z=4

x=3

y=2

z=4

400

y=x³-x

y=3x

(0,0),(-2,-6),(2,6)

500

x²+y²=90

y-x=6

(3,9), (-9,3)

Elimination

100

3x+2y=16

2x-2y=4

x=4

y=2

200

x+2y=11

5x+y=10

x=1

y=5

300

3x=4y+1

2x+4y=14

x=3

y=2

400

3x=2y+1

5x=4y-1

x=3

y=4

500

2x+2=6y

3x-2y=11

x=5

y=2

Matrix Operations

100

2 [[1,7],[5,3]]

[[2,14],[10,6]]

200

[[-3,2],[4,9]]+[[2,6],[-2,3]]

[[-1,8],[2,12]]

300

[[3,-5],[-2,7]]+[[-2,6],[3,-6]]

[[1,1],[1,1]]

400

3[[-2,0],[1,3]]+[[0,4],[1,-2]]

[[-6,4],[4,7]]

500

-2[[1,3],[3,-5]]+3[[-2,7],[4,-3]]

[[-8,15],[6,1]]

Factoring

100

x²+4x+3

(x+3)(x+1)

200

x²-6x+8

(x-4)(x-2)

300

2x²+11x+12

(2x+3)(x+4)

400

2x²-8x-10

(2x+2)(x-5)

500

15x²+8x-16

(5x-4)(3x+4)

Solving via Matrix

100

2x+y-z=8

    2y+z=14

    2y-3z=6

x=2

y=6

z=2

200

2x-y+3z=10

x+2y-3z=9

y-2z=1

x=4

y=7

z=3

300

2x+4y-2z = 24

x-3y+ 2z = -7

   2y - 3z = 4

x=4

y=5

z=2

400

2x-y+z=5

-x+2y+z=2

2x-2y+3z=5

x=3

y=2

z=1

500

3x-2y+z= 4

2x+3y-2z=11

-4x-6y+3z=-27

x=3

y=5

z=5