Gr. 10 Math Exam Notes
Math Exam Notes
Unit 1
The Method of Substitution
-Solving a linear system by substituting for one variable from one equation into the other equation
-To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step 4: Check your solution by substituting into both original equations, or into the statements of a word problem
-When given a question in words, begin by defining how variables are assigned
Investigate Equivalent Linear Relations and Equivalent Linear Systems
-Equivalent linear equations: equations that have the same graph
-Equivalent linear systems: pairs of linear equations that have the same point of intersection
-For any linear equation, an equivalent linear equation can be written by multiplying the equation by any real
-Equivalent linear systems have the same solution; the graphs of linear relations in the system have the same point of intersection
-Equivalent linear systems can be written by writing equivalent linear equations for either or both of the equations, or by adding or subtracting the original equations
The Method of Elimination
-Solving a linear system by adding or subtracting to eliminate one of the variables
-To solve a linear system by elimination: -Arrange the two equations so that like terms are aligned -Choose the variable you wish to eliminate -If necessary. Multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate -Add or subtract to eliminate one variable -Solve for the remaining variable -Substitute into one of the original equations to find the value of the other variable
Solving Problems Using Linear System
-You can solve linear systems
Unit 1
The Method of Substitution
-Solving a linear system by substituting for one variable from one equation into the other equation
-To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step 4: Check your solution by substituting into both original equations, or into the statements of a word problem
-When given a question in words, begin by defining how variables are assigned
Investigate Equivalent Linear Relations and Equivalent Linear Systems
-Equivalent linear equations: equations that have the same graph
-Equivalent linear systems: pairs of linear equations that have the same point of intersection
-For any linear equation, an equivalent linear equation can be written by multiplying the equation by any real
-Equivalent linear systems have the same solution; the graphs of linear relations in the system have the same point of intersection
-Equivalent linear systems can be written by writing equivalent linear equations for either or both of the equations, or by adding or subtracting the original equations
The Method of Elimination
-Solving a linear system by adding or subtracting to eliminate one of the variables
-To solve a linear system by elimination: -Arrange the two equations so that like terms are aligned -Choose the variable you wish to eliminate -If necessary. Multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate -Add or subtract to eliminate one variable -Solve for the remaining variable -Substitute into one of the original equations to find the value of the other variable
Solving Problems Using Linear System
-You can solve linear systems