Solving Linear Equations
Solve by substitution
-3x+y=6
5x+2y=23
(1,9)
1. If a system of equations appears parallel on a graph, what will the "solution" be? (100 points)
2. If a system of equations appears to look like just one line on a graph, what will the "solution" be? (100 points)
1. no solution
2. infinitely many solutions
Find the value of 2 numbers if their sum is 21 and their difference is 11.
16+5=21
16-5=11
|5x|+4=19
x=-3 and x=3
f(x) = {-1 if x<1
{2x-2 if x> or equal to 1
See Mrs. Erich (583)
Solve by substitution
4x+y=7
-6x+y=-3
(1,3)
solve by elimination
2x-4y=-10
3x+4y=5
1. add and then solve for x
2. use value of x to find value of y
solution: (-1,2)
DOUBLE THE POINTS if correct!
The senior classes at high school A and high school B planned separate trips to New York City. The senior class at high school a rented and filled 1 van and 6 buses with 372 students. High school B rented and filled 4 vans and 12 buses with 780 students. How many students can a van carry? How many students can a bus carry?
Let x = number of vans
y = number of buses
Then x + 6y = 372
4x + 12y = 780
Multiply the first equation by -4: -4x - 24y = -1488
4x + 12y = 780
Adding the equations, we get -12y = -708
y = 59
Substitute for y in the equation x + 6y = 372:
x + 6(59) = 372
x + 354 = 372
x = 18
ANSWER: Each van carries 18 people and each bus can transport 59 people.
|4x+2|-2=18
DOUBLE POINTS IF CORRECT.
-200 if incorrect.
no solution
f(x) = {-x+1 if x<0
{x if x> or equal to 0
See Mrs. Erich (583)
Solve by graphing
2x-y=2
2x+y=6
y=2x-2
y=-2x+6
solution: (2,2)
Solve by elimination
2x+5y=-24
3x-5y=14
2x+5y=-24
3x-5y=14
5x=-10
x=-2 (plug into original equation to find that y=-4)
solution: (-2,-4)
Kabir and Ayan went shopping for clothes. Kabir spent $145 on 3 pairs of shoes and 2 shirts. Ayan spent $170 on 2 pairs of shoes and 5 shirts.
Given that they got the exact same shoes and shirts, how much do the shoes cost and how much do the shirts cost?
shoes: 35
shirt: 20
|x+8|-5<2
x<-1 and x>-15
f(x) { -x if x<0
{ x+1 if x>or equal to 0
see Mrs. Erich (579)
Solve by graphing
2x+y=6
-x+y=3
1. find intercepts
2x+y=6 (x intercept: 3, y intercept: 6)
-x+y=3 (x intercept: -3, y intercept: 3)
2. graph and find solution (1,4)
-3x-4y=3
9x+12y=-27
no solution
One cable TV provider has a $60 start-up fee and charges $80 per month, and another charges a $160 start-up fee plus $70 per month. At what month will both charge the same amount and what will that charge be?
Both will charge $860 for 10 months.
Graph the system of linear inequalities:
y <2x-2
y>0.5x+1
see Mrs. Erich (571)
solve by substitution
5x-y=18
10x-2y=32
isolate y and then plug into other equation
36=32
no solution
solve by elimination
x-6y=7
-x+6y=-7
0=0
infinitely many solutions
The Straus family is deciding between 2 lawn-care services. Green Lawn charges a $49 startup fee and $29 per month. Yard Guard charges a $25 startup fee plus $37 per month. At what month will both charge the same amount, and what will that amount be?
Both will charge $136 for 3 months.
Graph the system of inequalities and say whether the following points are in the solution:
3x+8y>48
x+y<12
2,8 yes or no
1,4 yes or no
2,8 yes
1,4 no