Page 198 - Math Course 2 (Book 1)

Methods of Solving Systems of Equations

Mo. 6

Lesson 5
Let’s Begin

KEY CONCEPTS:
1. Determine the best method for solving Determine the Best Method
systems of equations.
2. Apply systems of linear equations.
Examples

FUND-RAISING
MO. 6 - L5a At a Boy Scout fund-raising dinner, Mr. Jones bought

Applying Methods of Solving 2 adult meals and 3 child meals for $23. Mrs.
Gomez bought 4 adult meals and 2 child meals for
Systems of Equations $34. All adult meals are the same price and all child
meals are the same price.

Concept Summary The following system can be used to represent this
situation.

Solving Systems of Determine the best method to solve the system of
Equations equations.
Method The Best Time to Use Then solve the system.
2x + 3y = 23
To estimate the solution, since 4x + 2y = 34
Graphing graphing usually does not give
an exact solution. For an exact solution, an algebraic method is
best. Since neither the coef cients of x nor the
if one of the variables in either coef cients of y are 1 or –1, you cannot use the
Substitution equation has a coef cient of 1 substitution method.
or –1
Since the coef cients are not the same for either x
if one of the variables has or y, you will need to use elimination with
Elimination Using opposite coef cients in the
Addition multiplication.
two equations.
Multiply the f rst equation by –2 so the coef cients
if one of the variables has of the x-terms are additive inverses. Then add the
Elimination Using same coef cient in the two
Subtraction equations.
equations.
2x + 3y = 23 –4x – 6y = –46 Multiply by –2.
4x + 2y = 34 (+) 4x + 2y = 34
if one of the coef cients are –4y = –12 Add the equations.
1 or –1and neither of the
Elimination Using variables can be eliminated by
Multiplication –4y = –12 Divide each side
simply adding or subtracting –4 –4 by –4.
the equations

y = 3 Simplify.

Now substitute 3 for y in either equation to f nd the 4x = 28 Simplify.
value of x. 4x = 28 Divide each side by 4.
4x + 2y = 34 Second equation 4 4
x = 7 Simplify.
4x + 2(3) = 34 y = 3
4x + 6 = 34 Simplify. The solution is (7, 3). So, adult
Answer meals cost $7 and child meals
4x + 6 – 6 = 34 – 6 Subtract 6 from each side.
cost $3.

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