Substitution: Infinitely Many, One, or No Solution?
Solve the systems of equations:
-3x + 4y = -2
y = -5
(-6, -5)
Solve the systems of equations:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
What strategy would be best?
14x + 2y = 26
-14x - 6y = -50
Elimination because the coefficients on x are the same number with opposite signs
Answer: (1,6)
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
Solve the systems of equations:
x -3y = 6
x + 3y = 12
(9,1)
What strategy would be best?
y = 4x + 3
y = 2x + 9
Substitution because both equations are in slope-intercept form
Answer: (3,15)
Solve the systems of equations:
y = -2x - 9
3x -6y = 9
(-3, -3)
Solve the systems of equations:
-6x - 10y = 4
6x + 10y = 0
No Solution
What strategy would be best?
x = 2y - 4
5x + 2y = 28
Substitution because one of the equations is already solved for a variable.
Answer: (4,4)
Solve the systems of equations:
-8x - 5y = -24
-x + y = 10
(-2, 8)
Solve the systems of equations:
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
What strategy would be best?
3x - 4y = 16
2x + 2y = 6
Elimination Method
Answer: (4,-1)
Solve the systems of equations:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions
Solve the systems of equations:
-15x + 6y = -36
4x - 3y = 11
(2, -1)
What method would be the best?
y = -6 - 4x
y = 3x + 8
Substitution put one of the equations into slope intercept form
Answer: (-2,2)
One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers.
(3,7)