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CCGPS Coordinate Algebra (2-4-13). UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities? Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12 Today’s Question: When is it better to use substitution than elimination for solving systems? - PowerPoint PPT Presentation
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CCGPS Coordinate Algebra (2-4-13)
UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities?Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12
Today’s Question:When is it better to use substitution than elimination for solving systems?Standard: MCC9-12.A.REI.6
Solve Systems of Equations by
Graphing
Steps1. Make sure each equation is
in slope-intercept form: y = mx + b.
2. Graph each equation on the same graph paper.
3. The point where the lines intersect is the solution. If they don’t intersect then there’s no solution.
4. Check your solution algebraically.
y = 3x – 12y = -2x + 3
1. Graph to find the solution.
Solution: (3, -3)
2 2 82 2 4x yx y
2. Graph to find the solution.
Solution: (-1, 3)
2 52 1
y xy x
No Solution
3. Graph to find the solution.
22 3 9x yx y
Solution: (-3, 1)
4. Graph to find the solution.
Solution: (-2, 5)
5. Graph to find the solution.
52 1yx y
Types of Systems There are 3 different types of systems of linear
equations
3 Different Systems:1) Consistent-independent2) Inconsistent3) Consistent-dependent
Type 1: Consistent-independent A system of linear equations having
exactly one solution is described as being consistent-independent.y
x
The system has exactly one solution at the point of intersection
Type 2: Inconsistent A system of linear equations having no
solutions is described as being inconsistent.y
x
The system has no solution, the lines are parallel
Remember, parallel lines have the same slope
Type 3: Consistent-dependent A system of linear equations having an
infinite number of solutions is described as being consistent-dependent.y
x
The system has infinite solutions, the lines are identical
So basically…. If the lines have the same y-intercept b,
and the same slope m, then the system is consistent-dependent
If the lines have the same slope m, but different y-intercepts b, the system is inconsistent
If the lines have different slopes m, the system is consistent-independent
Solve Systems of Equations by Substitution
Steps1. One equation will have either x or y by
itself, or can be solved for x or y easily.2. Substitute the expression from Step 1 into
the other equation and solve for the other variable.
3. Substitute the value from Step 2 into the equation from Step 1 and solve.
4. Your solution is the ordered pair formed by x & y.
5. Check the solution in each of the original equations.
CW/HW1. 6 11 2. 2 3 1
2 3 7 1
3. 3 5 4. 3 3 35 4 3 5 17
5. 2 6. 5 74 3
y x x yx y y x
y x x yx y y x
y y xx y
18 3 2 12x y
HW
Graphing and Substitution WS