4.1
Tell whether the ordered pair is a solution of the linear system:
(2,6)
x+y=8
3x-y=0
Yes
2+6=8
0=0
Solve the system by substitution:
x=17-4y
y=x-2
(-0.2,1.8)
Solve the system of linear equations using elimination:
5x+6y=50
x-6y=-26
(4,5)
Solve the system using any method:
y=-2x-4
y=2x-4
(0,-4)
Substitution
Tell whether the ordered pair is a solution of the inequality:
x+y<7; (2,3)
Yes
5<7
Tell whether the ordered pair is a solution of the linear system:
(-2.5,-4)
y=6x+11
2x+y=-9
Yes
-4=-4
-9=-9
Solve the system by substitution:
6x-9=y
y=-3x
(1,-3)
Solve the system of linear equations using elimination:
x+y=2
2x+7y=9
(1,1)
Solve the system using any method:
4x+3y=27
4x-3y=-27
(0,9)
Elimination
Tell whether the ordered pair is a solution of the system of linear inequalities:
(-5,2)
y<4
y>x+3
Yes
2<4
2>-2
Tell whether the ordered pair is a solution of the linear system:
(8,2)
x-y=6
2x-10y=4
No
6=6
-4=4
Solve the system by substitution:
-5x+6y=-11
6y=x+5
(4,1.5)
Solve the system of linear equations using elimination:
11x-20y=28
3x+4y=36
(8,3)
Solve the system using any method:
-18x+6y=24
3x-y=-2
No Solution
Substitution
Tell whether the ordered pair is a solution of the inequality:
2x-y>1; (4,2)
Yes
6>1
Tell whether the ordered pair is a solution of the linear system:
(-2,0)
y=-2x-4
y=x+4
No
0=2
0=0
Solve the system by substitution:
8x=5y+24
-9y=40-8x
(1.5,-4)
Solve the system of linear equations using elimination:
-10x+3y=1
-5x-6y=23
(-1,-3)
Solve the system using any method:
-2x+y=3
-4x+2y=6
Infinitely many solutions
Elimination
Tell whether the ordered pair is a solution of the system of linear inequalities:
(3,1)
y<x-1
y>2x-4
No
1<2
1>2
You collect $8 selling small and large smoothies. You sell a total of 3 smoothies. Small smoothies cost $2 and large smoothies cost $4. How many of each size did you sell?
2 small and 1 large
x= small smoothie x=2
y=large smoothie y=1
A group spends $227.50 to rent a total of 15 tubes. A 1-person tube costs $12.50 and a 2-person tube $20. How many of each type of tube does the group rent?
3 1-person tubes, 12 2-person tubes
x= 1-person tube x=3
y= 2-person tube y=12
A food truck sells sandwiches for x dollars and drinks for y dollars. A customer pays $41 for 3 sandwiches and 2 drinks. Another customer pays $34 for 2 sandwiches and 4 drinks. How much do sandwiches and drinks cost?
$12 per sandwich x=12
$2.50 per drink y=2.5
Is it possible for a system of linear equations to have exactly two solutions? Why or why not?
No, we work only with linear equations; they will only cross over once or never.
Tell whether the ordered pair is a solution of the system of linear inequalities:
(0,-2)
2x+y<-1
x-y>2
No
-2<-1
2>2