Choose the method
y = 3x + 1
3x + 2y + 4 = 0
Substitution
y = x + 2
y = 4x + 23
(-7, -5)
y=6x-11
-2x-3y=-7
(2, 1)
p-q=11
2p+q=19
(10, -1)
Find the sum of two numbers if their sum is 12 and their difference is 4.
(Set up the system, but do not solve)
x: first number, y: second number
x + y = 12
x - b = 4
(8, 4)
2y + 8 = 3x
3y - 1 = x
Substitution
y=3x-22
y=2x-15
(7, -1)
y=-3x+5
5x-4y=-3
(1, 2)
-4x-2y=-12
4x+8y=-24
(6, -6)
3 adult tickets and 1 child ticket costs $38. $52 is the price of 3 adult and 2 child tickets.
(Set up the system but do not solve)
a: adult ticket, c: child ticket
3a + 1c = 38
3a + 2c = 52
(8, 14)
t = 2(p + 3)
3p = t
Equal Values
y=-8
y=6x+10
(-3, -8)
4x-3y=18
-2 = y
(3, -2)
-2a-9b=-25
-4a-9b=-23
(-1, 3)
Flying with the wind a plane averaged 158 mph. Flying in the opposite direction with the same engine speed, but into the wind, the plane averaged 112 mph. Find the plane speed and the wind speed.
(Set up but do not solve)
p: plane speed, w: wind speed
p + w = 158
p - w = 112
2x - 4y = 5
3x + 8y = -4
Elimination with Multiplication
y=3
y=-2x-13
(-8, 3)
-5r +s=-3
3r-8s=24
(0, -3)
5x+y=9
10x-7y=-18
(1, 4)
A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
B: Boat speed, C: Current speed
B+C=168/12
B-C=168/14
B = 26, C=2
5j + 2k = 3
2j + 3k = -2
Elimination with multiplication
q=-3p-9
q=2p+11
(-4, 3)
-3p+3q=4
-p =3-q
No solution
-7x+y=-19
-2x+3y=-19
(2, -5)
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
x: first digit, y: second digit
y+x=-1
10y+x=10x+y+9
34, (x=3, y=4)