Substitution
2x+4y=42
3x+y=8
(-1,11)
3x-3y=18
-9x+14y=-6
(15.6,9.6)
(234/15,48/5)
2x+8y=1
x=2y
(1/6,1/12)
x+y=1
x-2y=-8
(-2,3)
Greg is a star player on a basketball team. In one game, his field-goal total was 20 points, made up of 2-pointers and 3-pointers. If he made a total of 9 baskets, how many of each did he make?
7 2s, and 2 3s
3m+6n=12
4m+5n=28
(12,-4)
x+3y=-9
4y=x+16
(-12,1)
y=2x-4
7x-5y=14
(2,0)
5x+2y=24
2x-12=4y
(5,-1/2)
Amanda is planning a cookout. She has budgeted a maximum of $60 for hamburgers, and turkey dogs. Hamburgers cost $3 per pound, and turkey dogs cost $2 per pound. Write an inequality that describes the possible number of pounds of hamburgers and turkey dogs she can purchase.
3x+2y<=60
-3x+6y=18
y=1/2x+3
Infinite
-3(5+x)=y
5(x-3)=2y+4
(-1,-12)
x+y+z=7
2x+3y=3
x=-2y
(6,-3,4)
1/3x-y=4
2x-6y=12
no solution
The sum of two numbers is 7. Four times the first number is one more than five times the second. Find the two numbers by setting up a system of equations and solving by substitution.
4 and 3
1/2x-1/3y=1/6
6x-4y=1
No solution
5x-28/3y=2
-3x=4y
(1/6,-1/8)
2x-3y=1
y=x-2
(5,3)
4x+3y=0
y-x=-7
(3,-4)
Three blouses and four skirts are on sale for $72.50. Five blouses and two skirts would cost $66.00. Find the cost of one blouse and one skirt by setting up a system of equations and solving by elimination or substitution.
$8.50 blouse
$11.75 skirt
2x+3y=3
-6x-12y=-11
(1/2,2/3)
2b=2a+b-4
3a=3b-a+2
4.5x-3y=-1.65
-2x+1.5y=0.8
(-9/25,1/3)
8n=6m+3
9m=12n-4.5
Infinite
Misha has a 2500-meter spool of rope that he must cut into 50-meter and 75-meter lengths for his rock-climbing class. Write an inequality that will express the possible numbers of each length he can cut from his spool of rope.
50x+75y<=2500