Investigation
How many solutions does this system have?
y = 2x + 7
y = 3x + 8
What is one solution?
Substitute into the second equation for the variable x.
x = 5
y = x + 35
y = 5+35
y = 40
Isolate the "y" variable in the following equation.
x + y = 29
y = -x + 29
Check if the ordered pair (1, 1) is the solution to the system of equations.
3x + 9y = 12
3= -3x + 6y
Yes, this is the correct solution!
How do you write the solution to a system of equations?
- One solution: (x, y)
- Infinite OR No Solutions: just write "infinite solutions" or "no solutions"
How many solutions does this system have?
y = 4x + 8
y = 4x + 25
What is no solution? (parallel lines!)
Substitute into the second equation for the variable y.
y = 4x
y + 2x = 10
4x + 2x = 10
6x = 10
Isolate the "x" variable in the following equation.
2x + 4y = 16
x = -2y + 8
Check if the ordered pair (2, 1) is the solution to the system of equations.
6x - y = -13
x + y = -1
No, it is not the correct solution.
Knowing x=4 in a system, use the equation below to find what y is equal to.
y = 3x -4
y = 8
How many solutions does this system have?
y = 3x + 8
3y = 9x + 24
What is infinite solutions? (they are the same line!)
Substitute into the second equation for the variable y.
y = 2x + 1
2y = 15x + 20
2(2x + 1) = 15x + 20
4x + 2 = 15x + 20
Isolate the "y" variable in the following equation.
12x - y = -20
y = 12x + 20
Check if the ordered pair (2, 4) is the solution to the system of equations.
4x = -8y
-4x - 4y = 1
No, it is not the correct solution.
Fill in the blank......
Equations with different slopes will have ______ solution(s).
What is "one" solution?
How many solutions does this system have?
x = 5
y = -35
What is one solution?
Substitute into the second equation for the variable x.
x = 3y - 2
2y = 3x + 30
2y = 3(3y - 2) + 30
2y = 9y - 6 + 30
2y = 9y + 24
Isolate the "y" variable in the following equation.
4x - 2y = 18
y = 2x - 9
Check if the ordered pair (-2, 1) is the solution to the system of equations.
-7x + 5y = 19
4x - 5y = -13
Yes, it is the correct solution!
When solving by substitution, your last step is as follows.... "28 = 28".
How many solutions does your system have?
What is infinitely many solutions?
How many solutions does this system have?
y - x = 18
4y = 4x + 72
What is infinite solutions? (they are the same line)
Substitute into the second equation for the variable y.
y = 12x + 9
3y + 4x = 28
3(12x + 9) + 4x = 28
36x + 27 + 4x = 28
40x + 27 = 28
Isolate the "x" variable in the following equation.
-5x - 10y - 45 = 0
x = -2y - 9
Check if the ordered pair (-3, -2/3) is the solution to the system of equations.
2x - 3y = -4
-4x + 3y = 10
Yes, it is the correct solution!
Knowing y = 3/2 in a system, use the equation below to find what x is equal to.
2y - 5x - 1 = 0
y = 2/5 OR y = 0.4