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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. 5 - Systems and Matrices문제 100
6장, 문제 100

Solve each problem. See Examples 5 and 9. At the Berger ranch, 6 goats and 5 sheep sell for \$305, while 2 goats and 9 sheep sell for \$285. Find the cost of a single goat and of a single sheep.

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1
Define variables to represent the unknowns: let \(g\) be the cost of one goat and \(s\) be the cost of one sheep.
Translate the problem into a system of linear equations based on the given information: \(6g + 5s = 305\) \(2g + 9s = 285\)
Choose a method to solve the system (substitution or elimination). For elimination, multiply the equations to align coefficients for either \(g\) or \(s\) so you can eliminate one variable by addition or subtraction.
Perform the multiplication and then add or subtract the equations to eliminate one variable, resulting in a single equation with one variable.
Solve the single-variable equation for that variable, then substitute back into one of the original equations to find the value of the other variable.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. Solving the system means finding values for the variables that satisfy all equations simultaneously. In this problem, the prices of goats and sheep are variables, and the given total costs form the equations.
추천 영상:
가이드 코스
4:27
Introduction to Systems of Linear Equations

Setting Up Equations from Word Problems

Translating a word problem into mathematical equations involves identifying quantities and their relationships. Here, the number of goats and sheep and their total costs are used to form equations representing the problem. Accurate translation is essential for solving the system correctly.
추천 영상:
06:00
Categorizing Linear Equations

Methods for Solving Systems (Substitution or Elimination)

Common methods to solve systems include substitution, where one variable is expressed in terms of another, and elimination, where equations are added or subtracted to eliminate a variable. Applying these methods helps find the individual prices of goats and sheep efficiently.
추천 영상:
가이드 코스
5:48
Solving Systems of Equations - Substitution
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교과서 질문

Solve each problem. See Examples 5 and 9. A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is \$351. How many of each denomination of bill are there?

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교과서 질문

Solve each problem. See Examples 5 and 9. Solve the system of equations (4), (5), and (6) from Example 9.

25x+40y+20z=220025x + 40y + 20z = 2200 (4)

4x+2y+3z=2804x + 2y + 3z = 280 (5)

3x+2y+z=1803x + 2y + z = 180 (6)

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교과서 질문

Find AB and BA for the following matrices.

A=[abcd]andB=[1001]A = \(\left\)[ \(\begin{matrix}\) a & b \\ c & d \(\end{matrix}\) \(\right\)] \(\quad\) \(\text{and}\) \(\quad\) B = \(\left\)[ \(\begin{matrix}\) 1 & 0 \\ 0 & 1 \(\end{matrix}\) \(\right\)]

Matrix B acts as the multiplicative element for 2 ×\(\times\) 2 square matrices.

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교과서 질문

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

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교과서 질문

Find the inverse, if it exists, for each matrix.

[2−101011−20]\(\left\)[ \(\begin{matrix}\) 2 & -1 & 0 \\ 1 & 0 & 1 \\ 1 & -2 & 0 \(\end{matrix}\) \(\right\)]

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교과서 질문

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

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