Post on 18-Jan-2016
Systems of equations- two equations together A solution of a system of equations is an ordered pair that
satisfies both equations
Consistent- the graphs of the equations intersect If consistent with exactly 1 solution = independent If consistent with infinite solutions = dependent
Inconsistent- the graphs of the equations are parallel No ordered pair solutions
Exactly one solution
Infinite solutions
No solutions
Consistent and Independent
Consistent and Dependent
Inconsistent
3.1
Ex: Solve by graphing
y = -x + 8
y = 4x - 7
*See teacher or other student class for work on these examples
Ex #2. Solve by graphing
x + 2y = 5
2x + 4y = 2
*See teacher or other student class for work on these examples
Substitution Method: used when one equation can be solved for a variable. When one variable has a coefficient of 1 or -1
Elimination Method: used when the two equations have the same coefficient for one of the variables (you can add or subtract right away to cancel one variable)
Elimination with Multiplication Method: used when substitution and elimination don’t work
3.2
Substitutionx + 5y = -33x – 2y = 8
Infinite or No solutions
6x – 2y = -4y = 3x + 2
Write and solve a System of Equations
The New York Yankees and Cincinnati Reds together have won a total 31 World Series. The Yankees have won 5.2 times as many as the Reds. How many have each team won?6x – 2(3x +2) = -
46x – 6x - 4 = -4-4 = -4
When all variables cancel, if:
the statement is true = infinite solutions
the statement is false = no solutions
Infinite solutions
Elimination5s + 2t = 69s + 2t = 22
Write and solve a system of equationsTwice one number added to another number is 18. Four times the
first number minus the other number is 12. Find the numbers.
Multiply One Equation3x + 4y = 65x + 2y = -4
Multiply Two Equations3x + 4y = -252x – 3y = 6
Multiply one equation to make a variable have the same number and opposite sign
Multiply both equations to make a variable have the same number and opposite sign
1. get the inequality in slope-intercept from2. Graph the intercept and use slope to find
the next points3. Draw the line: < or > = dotted, or
= solid4. If needed: Test an ordered pair not on the
line-if true, shade that side of the line-if false, shade the other side of the line
5. Repeat steps 1-4 for the second inequality.
3.3
2
32
xy
xy
834
434
xy
xy
4
632
22
y
yx
xy