Equation of a Line
100- 12x + 4y - 3 = 17
A- y = -3x + 5
x+y=14 x-y=4
y=14-x
x-(14-x)=4 x-14+x=4 2x=14+4
2x=18 x=9
y=14-9 y=5
POI= (9,5)
The sum of Abdul’s and Josh’s ages is 36 Josh is 4 years younger than Abdul. How old are they?
x+(x+4)=36
Josh is 16
Abdul is 20
200- 12x - 6y + 37 = -11
A- y = 2x + 8
3x-y=3 9x-3y=9
y=3x-3 9x-3(3x-3)=9
9x-9x+9=9
0x=0 y=-3
POI (0,-3)
Diljeet has 21.5 more Cardboard boxes than Will in total they have 37.5 Cardboard boxes. How many Cardboard boxes does Diljeet have? How many Cardboard boxes does Will have?
(x+21.5)+x=37.5
Diljeet has 29.5 cardboard boxes
Will has 8 cardboard boxes
y=-7x+3 y=-5x+5
-7x+3=-5x+5
-7x+5x=5-3 -2x=2 x=-1
y=-5(-1)+5
y=10
POI= (-1,10)
Ben is hiking and took 2 hours to travel 24 km down a steep hill. The return trip (up the hill) took 3 hours. What was the speed of the Ben? How much difference was the hill making to Ben's pace?
x=Bens hiking speed
y=The difference the hill is making to his speed
Ben took 2 hrs to travel 24 km at a specific speed while going down a hill.
x+y=12 km/h
Ben 3 hrs to travel 24 km at a specific speed while hiking up a hill.
x-y= 8 km/h
speed=10 km/h
Diffrence the hill made=2 km/h
-3x=-5y+7 2y=x-5
x=2y+5 -3(2y+5)=-5y+7
-6y+-15=-5y+7 -6y+5y= 7+15
-y=22 y=-22
x=2(-22)+5 x=-44=5 x=-39
POI (-39,-22)
Luch needs to make 10L of 42% bubbles for Mop bucket.The Soap solutions available are 30% soap and 50% soap. How many liters of each soap are needed to make the 42% soap?
30% soap=y
50% soap=x
He needs 10 L total
x+y=10L
30% soap and 50% soap combine to make 10L of 42% bubbles
0.3x+0.5y=4.2
Luch needs 6L of 50% soap and 4L of 30% soap
-x + 5x + 4y - 2y + 19 = 7
A: y = -2x - 6
2x+y=5 x-2y=-1
x=-1+2y 2(-1+2y)+y=5 -2+4y+y=5
-2+5y=5 5y=7 y=7/5 1.4
x=-1+2(7/5) x=9/5 1.6
POI (9/5,7/5)
Jason invests his summer earnings of $3050. He invests part of the money at 8% per year and the rest at 7.5% per year. After one year these investments make $242 in simple interest. How much did he invest at each year?
x=8%
y=7.5%
He invests 3050 total
x + y=3050
He made $242 between his investments
0.08x+0.075y=242
Jason invested $400 into the 7.5% account and $2,650 into the 8% Account