In this chapter, you will learn:
- How to write and solve mathematical sentences (such as one- and two-variable equations) to solve situational word problems.
- Methods to solve systems of equations in different forms.
- What it means for a system to have no solutions or infinite solutions.
- Ways to know which solving method is most efficient and accurate.
Writing An Equation:
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Summary of Methods to Solve Systems:
Method This Method is Most Efficient When Example
Equal Values Both equations in y-form. y = x - 2
y = -2x +1
Substitution One variable is alone on one side y = -3x - 1
of one equation. 3x + 6y = 24
Elimination: Equations in standard form with x + 2y = 21
Add opposite coefficients. 3x - 2y = 7
Elimination: Equations in standard form. One x + 2y = 3
Multiply equation can be multiplied to create 3x + 2y = 7
opposite terms.
Elimination: When nothing else works. Example, 2x - 5y = 3
Multiply Both multiply first equation by 3, multiply the 3x +2y = 7
second by -2, and finally add.
Equal Values Both equations in y-form. y = x - 2
y = -2x +1
Substitution One variable is alone on one side y = -3x - 1
of one equation. 3x + 6y = 24
Elimination: Equations in standard form with x + 2y = 21
Add opposite coefficients. 3x - 2y = 7
Elimination: Equations in standard form. One x + 2y = 3
Multiply equation can be multiplied to create 3x + 2y = 7
opposite terms.
Elimination: When nothing else works. Example, 2x - 5y = 3
Multiply Both multiply first equation by 3, multiply the 3x +2y = 7
second by -2, and finally add.