Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Signal-flow graph wikipedia , lookup

Horner's method wikipedia , lookup

Quartic function wikipedia , lookup

Cubic function wikipedia , lookup

System of linear equations wikipedia , lookup

Elementary algebra wikipedia , lookup

System of polynomial equations wikipedia , lookup

Equation wikipedia , lookup

History of algebra wikipedia , lookup

Transcript
```Mr. Sims
- need to be able to add the 2 equations together
and cancel out one of the variables
1.
-3x + 2y = -6
5x – 2y = 18
2x
Algebra 2
Section 10.2 C
and the y’s will cancel
= 12
x=6
substitute into any equation
with x and y to solve for y
-3x + 2y = -6
-3(6) + 2y = -6
-18 + 2y = -6
+18
+18
2y = 12
y=6
Mr. Sims
2 . -1 3x + 5y = -16
3x – 2y = -9
multiply either top or bottom
by a term, so that, when added
a variable cancels out
-3x – 5y = 16
3x – 2y = -9
-7y = 7
y = -1
substitute into any equation
with x and y to solve for x
3x + 5y = -16
3x + 5(-1) = -16
3x – 5 = -16
+5
+5
3x = -11
11
x
3
Mr. Sims
3.
5 4x – 3y = 0
2 -10x + 7y = -2
multiply either top, bottom, or both
by a term, so that, when added
a variable cancels out
20x – 15y = 0
-20x + 14y = - 4
-y=-4
y=4
substitute into any equation
with x and y to solve for x
4x – 3y = 0
4x – 3(4) = 0
4x – 12 = 0
+12 +12
4x = 12
x=3
Mr. Sims
4. 2 -6x + 5y = 4
7x – 10y = -8
-12x + 10y = 8
7x – 10y = -8
-5x = 0
x=0
substitute
-6x + 5y = 4
-6(0) + 5y = 4
5y = 4
4
y
5
Mr. Sims
5. 4 -9x + 6y = 0
-3 -12x + 8y = 0
-36x + 24y = 0
36x – 24y = 0
0=0
always true
infinitely many solutions
Mr. Sims
6. 5 21x – 8y = -1
8 9x + 5y = 8
105x – 40y = -5
72x + 40y = 64
177x = 59
59
x
177
1
x
3
substitute
9x 5y  8
1
9   5y  8
 3
3 + 5y = 8
-3
-3
5y = 5
y=1
Mr. Sims
1.) 3x – 2y = 10
5x + 3y = -15
2.) 2y + 3x – 8.1 = 0
2x – 3y + 3.7 = 0
Algebra 2
Section 10.2 C