Puzzle time algebra 1

Part a)

3x+2y=12------> equation 1

y=x-9------> equation 2

substitute equation 2 in equation 1

3x+2*[x-9]=12-----> 3x+2x-18=12----> 5x=30------> x=6

y=6-9-----> y=-3

the answer part a) is

(6,-3)-------> word-----> HE

Part b)

4x+y=-2-----> equation 1

y=2x-2-----> equation 2

substitute equation 2 in equation 1

4x+[2x-2]=-2-----> 6x=0----> x=0

y=2*0-2-----> y=-2

the answer part b) is

(0,-2)-------> word-----> MADE

Part c)

-3x+5y=5-----> equation 1

y=x-1------> equation 2

substitute equation 2 in equation 1

-3x+5*[x-1]=5-----> -3x+5x-5=5----> 2x=10-----> x=5

y=5-1-----> y=4

the answer Part c) is

(5,4)-------> word-----> A

Part d)

2x+y=-16-----> equation 1

y=2x---> equation 2

substitute equation 2 in equation 1

2x+[2x]=-16-----> 4x=-16-----> x=-4

y=2*(-4)-----> y=-8

the answer Part d) is

(-4,-8)-------> word-----> KNOT

Part e)

7x=-35------> x=-5

-8x+9y=4-----> -8*(-5)+9y=4-----> 40+9y=4----> 9y=-36-----> y=-4

the answer Part e) is

(-5,-4)-------> word-----> IN

Part f)

-4x+3y=20-----> equation 1

-14y=-56----> y=4

substitute in equation 1

-4x+3*4=20-----> -4x=8----> x=-2

the answer Part f) is

(-2,4)-------> word-----> HIS

Part g)

13x-6y=-5------> equation 1

x+10=11-----> x=1

13*1-6y=-5------> -6y=-5-13-----> y=3

the answer Part g) is

(1,3)-------> word-----> TAIL

Part h)

9x-2y=12----> equation 1

y+4=16------> y=12

9x-2*12=12-----> 9x=36----> x=4

the answer Part h) is

(4,12)-------> word-----> AND

Part i)

x=6+2y------> equation 1

-3x+14y=-18------> equation 2

substitute equation 1 in equation 2

-3*[6+2y]+14y=-18------> -18-6y+14y=-18----> 8y=0-----> y=0

x=6+2*0-----> x=6

the answer Part i) is

(6,0)-------> word-----> CALLED

Part j)

5x-9y=12-----> equation 1

y=-6-x-----> equation 2

substitute equation 2 in equation 1

5x-9*[-6-x]=12-------> 5x+54+9x=12-----> 14x=-42------> x=-3

y=6-(-3)----> y=-3

the answer Part j) is

(-3,-3)-------> word-----> IT

Part k)

x=-8+y------> equation 1

6x+y=-6------> equation 2

substitute equation 1 in equation 2

6*[-8+y]+y=-6-----> -48+6y+y=-6-----> 7y=42-----> y=6

x=-8+6-----> x=-2

the answer Part k) is

(-2,6)-------> word-----> A

Part l)

7x-3y=17----> equation 1

y=2x-6------> equation 2

substitute equation 2 in equation 1

7x-3*[2x-6]=17------> 7x-6x+18=17-----> x=-1

y=2*(-1)-6----> y=-8

the answer Part l) is

(-1,-8)-------> word-----> PIGS

part m)

The physical education instructor asked each student to do a total of 36 pull-ups and push-ups in 1 minute. The instructor wanted students to do 8 times as many push-ups as pull-ups. Write a system of linear equations that represents this situation. How many pull-ups and push-ups were required in 1 minute?

let

x-------->pull-ups

y------->push-ups