Download - Example 2: Solve the system
4.2 Solving Systems of Linear Equations by Substitution with work
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4.2 Solving Systems of Linear Equations by Substitution
OBJECTIVE 1: Using the Substitution MethodGraphing is a great way to get a visual image of what to expect for your graph, but not always an accurate way. A more accurate method for solving systems of equations is the substitution method where you replace part of an equation into the other equation.
Example 1: Solve the system. 2x + y = 10
x = y + 2
Practice 1: Solve the system. 2x y = 9
x = y + 1
Example 2: Solve the system.5x y = 2
y = 3x
Practice 2: Solve the system.7x y = 15
y = 2x
4.2 Solving Systems of Linear Equations by Substitution with work
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Example 3: Solve the system: x + 2y = 7
2x + 2y = 13
Practice 3: Solve the system: x + 3y = 6
2x + 3y = 10
Solving a System of Two Linear Equations by the Substitution Method
STEP 1: Solve one of the equations for one of its variables.
STEP 2: Substitute the expression for the variable found in STEP 1 into the other equation.
STEP 3: Solve the equation from STEP 2 to find the value of one variable.
STEP 4: Substitute the value found in STEP 3 in any equation containing both variables to find the value of the other variable.
STEP 5: Check the proposed solution in the original system.
4.2 Solving Systems of Linear Equations by Substitution with work
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Concept CheckAs you solve the system, to the right, you find that y = 5. Is this the solution of the system?
2x + y = 5
x y = 5
Example 4: Solve the system.7x 3y = 14
3x + y = 6
Practice 4: Solve the system.5x + 3y = 9
2x + y = 8
4.2 Solving Systems of Linear Equations by Substitution with work
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Concept CheckTo avoid fractions, which of the equations below would you use to solve for x?
a) 3x 4y = 15 b) 14 3y = 8x c) 7y + x = 12
Example 5: Solve the system.
x y = 312x = 6 + 2y
Practice 5: Solve the system. 14x y = 2x = 4y + 8
4.2 Solving Systems of Linear Equations by Substitution with work
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Example 6: Use substitution to solve the system. 6x + 12y = 5
4x 8y = 0
Practice 6: Use substitution to solve the system. 4x 3y = 12
8x + 6y = 30
Concept CheckDescribe how the graphs of the equations in a system appear if the system has
a) no solution
b) one solution
c) an infinite number of solutions
4.2 Solving Systems of Linear Equations by Substitution with work
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4.2 Assignment p. 267
9 47 (o), 53, 57