Solving Linear Equations
How many solutions?
Graphical Solutions
System of Linear Equations
100
9(3 - 2x) = 2(10 - 8x)
What is 7⁄2?
27 - 18x = 20 - 16x
7 - 18x = -16x
7 = 2x
7⁄2 = x
27 - 18x = 20 - 16x
7 - 18x = -16x
7 = 2x
7⁄2 = x
100
1⁄2(2x + 4 + 8x) = 1⁄3(4 + x)
Show work to justify your answer!! :-)
Show work to justify your answer!! :-)
What is one solution?
1⁄2(10x + 4) = 1⁄3(4 + x)
5x + 2 = 1⁄3(4 + x)
15x + 6 = 4 + x
14x + 6 = 4
14x = -2
x = -2⁄14 = -1⁄7
or
1⁄2(10x + 4) = 1⁄3(4 + x)
5x + 2 = 1⁄3(4 + x)
5x + 2 = 4⁄3 + 1⁄3x
15⁄3x + 6⁄3 = 4⁄3 + 1⁄3x
14⁄3x + 6⁄3 = 4⁄3
14⁄3x = -2⁄3
x = -2⁄14=-1⁄7
1⁄2(10x + 4) = 1⁄3(4 + x)
5x + 2 = 1⁄3(4 + x)
15x + 6 = 4 + x
14x + 6 = 4
14x = -2
x = -2⁄14 = -1⁄7
or
1⁄2(10x + 4) = 1⁄3(4 + x)
5x + 2 = 1⁄3(4 + x)
5x + 2 = 4⁄3 + 1⁄3x
15⁄3x + 6⁄3 = 4⁄3 + 1⁄3x
14⁄3x + 6⁄3 = 4⁄3
14⁄3x = -2⁄3
x = -2⁄14=-1⁄7
100
How many solutions do the equations/lines in the following graph have?
What is no solution?
100
Solve for the following system of linear equations:
y = 5
y = 3x + 2
y = 5
y = 3x + 2
What is (1, 5)?
y = 5
5 = 3x + 2
3 = 3x
1 = x
y = 5
5 = 3x + 2
3 = 3x
1 = x
200
3x + 2x + 9 = 1⁄3(9x + 3x + 27)
What is x = 0?
3x + 2x + 9 = 3x + x + 9
5x + 9 = 4x + 9
5x = 4x
x = 0
3x + 2x + 9 = 3x + x + 9
5x + 9 = 4x + 9
5x = 4x
x = 0
200
3x + x + 9 = 1⁄3(9x + 3x +27)
Show work to justify your answer!! :-)
Show work to justify your answer!! :-)
What is infinitely many solutions?
4x + 9 = 1⁄3(12x +27)
4x + 9 = 4x + 9
4x = 4x
x = x
4x + 9 = 1⁄3(12x +27)
4x + 9 = 4x + 9
4x = 4x
x = x
200
How many solutions do the equations/lines in the following graph have?
What is one solution?
200
Solve for the following system of linear equations:
y = 9x + 2
y = 3x + 2
y = 9x + 2
y = 3x + 2
What is (0, 2)?
They share the same y-intercept, so the solution is (0, 2).
or
Solve for x:
9x + 2 = 3x + 2
9x = 3x
3x = 0
x = 0
Solve for y:
y = 9(0) + 2
y = 2
They share the same y-intercept, so the solution is (0, 2).
or
Solve for x:
9x + 2 = 3x + 2
9x = 3x
3x = 0
x = 0
Solve for y:
y = 9(0) + 2
y = 2
300
3⁄2(x + 2 + x) = 8 + x
What is x = 5⁄2?
3⁄2(2x + 2) = 8 + x
3x + 3 = 8 + x
2x + 3 = 8
2x = 5
x = 5⁄2
3⁄2(2x + 2) = 8 + x
3x + 3 = 8 + x
2x + 3 = 8
2x = 5
x = 5⁄2
300
23x + 3 = 2(4x + 1)
Show work to justify your answer!! :-)
Show work to justify your answer!! :-)
What is no solution?
8x + 3 = 2(4x + 1)
8x + 3 = 8x + 1
3 = 1
3 ≠ 1
8x + 3 = 2(4x + 1)
8x + 3 = 8x + 1
3 = 1
3 ≠ 1
300
What is the solution to the equations/lines in the following graph?
What is (2, -1)?
300
Solve for the following system of linear equations:
y = 18x + 2
y = 1⁄2(36x + 4)
y = 18x + 2
y = 1⁄2(36x + 4)
What is infinitely many solution?
18x + 2 = 1⁄2(36x + 4)
18x + 2 = 18x + 2
18x = 18x
x = x
18x + 2 = 1⁄2(36x + 4)
18x + 2 = 18x + 2
18x = 18x
x = x
400
y = 1⁄3x + 10
If y = 5, solve for x.
If y = 5, solve for x.
What is x = -15?
5 = 1⁄3x + 10
-5 = 1⁄3x
-15 = x
-5 = 1⁄3x
-15 = x
400
18x + 5 = -2x(7 + 1)
Show work to justify your answer!! :-)
Show work to justify your answer!! :-)
What is one solution?
18x + 5 = -2x(8)
18x + 5 = -16x
34x + 5 = 0
34x = -5
x = -5⁄34
18x + 5 = -2x(8)
18x + 5 = -16x
34x + 5 = 0
34x = -5
x = -5⁄34
400
How many solutions do the equations/lines in the following graph have? Note: The two lines overlap each other.
What is infinitely many solutions?
400
Solve for the following system of linear equations:
2x - y = 5
2x + y = 3
2x - y = 5
2x + y = 3
What is (2, -1)?
2x - y = 5 → y = 2x - 5
2x + y = 3 → y -2x + 3
Solve for x:
2x - 5 = -2x + 3
4x - 5 = 3
4x = 8
x = 2
Solve for y:
y = 2(2) - 5
y = 4 - 5
y = -1
2x - y = 5 → y = 2x - 5
2x + y = 3 → y -2x + 3
Solve for x:
2x - 5 = -2x + 3
4x - 5 = 3
4x = 8
x = 2
Solve for y:
y = 2(2) - 5
y = 4 - 5
y = -1
500
y = 2⁄5x + 7
Find the y-intercept and the x-intercept.
Find the y-intercept and the x-intercept.
What is 7 for the y-intercept and -35⁄2 for the x-intercept?
x-intercept
0 = 2⁄5x + 7
-7 = 2⁄5x
-35⁄2=x
x-intercept
0 = 2⁄5x + 7
-7 = 2⁄5x
-35⁄2=x
500
Who was the youngest US President?
What is Theodore(Teddy) Roosevelt at the age of 42?
Teddy became president after President McKinley was assassinated in 1901.
Teddy became president after President McKinley was assassinated in 1901.
500
In Toy Story, who was the voice actor for Woody?
What is Tom Hanks?
500
Who is Spider-man?
What is Peter Parker?