Equal Values Method
Substitution Method
Elimination Method
Solving for a Variable
How Many Solutions?/Let Statements
100
y = −x + 8 y = x − 2
( 5, 3 )
100
y = 2x - 3 x + y = 15
( 3,5 )
100
x − y = 11 2x + y = 19
( 10, -1 )
100
Solve for y: 2x − y = 10
y = 2x - 10
100
y = 6x + 5 y = 6x - 3
No Solution
200
k = -6p + 18 k = 3p - 9
p = 3 k = 0
200
y=3−x y = 4x + 3
( 0,3 )
200
−4x − 2y = −12 4x + 8y = −24
( 6,-6)
200
Solve for y: 2y - 4x = 8
y = 2x + 4
200
y = 3x - 5 y = 3x - 5
Infinitely Many Solutions
300
x = 3y + 2 x = y + 2
( 2,0 )
300
c = -b -11 3c + 6 = 6b
c = -8 b = -3
300
3x + y = 1 x + y = 3
( -1,4 )
300
Solve for m: 2(m − 3) = 4(m + 1)
m = -5
300
2y = 2x + 8 y = x + 4
Infinitely Many Solutions
400
y = x + 4 2x + y = 7
( 1,5 )
400
y = - x - 7 5y + 3x = -13
( -11,4 )
400
2x + 5y = 16 5x - 2y = 11
( 3,2 )
400
Solve for y: 2x−4y=12
y = (1/2)x - 3
400
Let Statement: The Fabulous Footballers scored an incredible 55 points during last night’s game. Interestingly, the number of field goals was one more than twice the number of touchdowns. The Fabulous Footballers earned seven points for each touchdown and three points for each field goal. How many touchdowns and field goals did the Fabulous Footballers score?
Let t = the number of touchdowns Let f = the number of field goals
500
x + 2y = 4 x + 2y = 6
No Solution
500
y = x - 3 2(x+y) = 18
( 6,3 )
500
4x + 3y = 10 9x − 4y = 1
( 1,2 )
500
Solve for x: (x + 6)(x − 3) = x^2 + 9
x = 9
500
Let Statement: Barbara has a bunny that weighs 5 pounds and gains 3 pounds per year. Her cat weighs 19 pounds and gains 1 pound per year. When will the bunny and the cat weight the same?
Let x = time (years) Let y = weight (pounds)
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