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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblem 25
Chapter 6, Problem 25

In Exercises 19–30, solve each system by the addition method. 4x + 3y = 15 2x - 5y = 1
Exercise 25: Solve the system of equations 4x + 3y = 15 and 2x - 5y = 1 using the addition method.

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1
Multiply the second equation by 2 to align the coefficients of x: 2(2x - 5y) = 2(1)
This results in the equation: 4x - 10y = 2
Now, add the two equations together: (4x + 3y) + (4x - 10y) = 15 + 2
Combine like terms: 4x + 4x + 3y - 10y = 17
Simplify the equation to find the value of y: 8x - 7y = 17

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The solution is the set of values for the variables that satisfy all equations simultaneously. Understanding how to interpret and represent these systems is fundamental to solving them.
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Addition (Elimination) Method

The addition method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable. This requires manipulating the equations, often by multiplying by constants, to align coefficients for elimination.
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Solving for Variables After Elimination

Once one variable is eliminated, the resulting single-variable equation can be solved using basic algebra. After finding this variable's value, substitute it back into one of the original equations to find the other variable, completing the solution.
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Related Practice
Textbook Question

Solve each system in Exercises 25–26. {x+26−y+43+z2=0x+12+y−12−z4=92x−54+y+13+z−22=194\(\begin{cases}\[\frac{x + 2}{6}\) - \(\frac{y + 4}{3}\) + \(\frac{z}{2}\) = 0 \(\frac{x + 1}{2}\) + \(\frac{y - 1}{2}\) - \(\frac{z}{4}\) = \(\frac{9}{2}\) \(\frac{x - 5}{4}\) + \(\frac{y + 1}{3}\) + \(\frac{z - 2}{2}\) = \(\frac{19}{4}\]\end{cases}\)

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Textbook Question

Graph each inequality. y≥log2(x+1)

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Textbook Question

Write the partial fraction decomposition of each rational expression. x2+2x+7/x(x − 1)2

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Textbook Question

In Exercises 19–28, solve each system by the addition method. {x2+y2=25(x−8)2+y2=41\(\begin{cases}\)x^2 + y^2 = 25 \\(x - 8)^2 + y^2 = 41\(\end{cases}\)

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Textbook Question

Solve each system by the method of your choice.

{5y=x2−1x−y=1\(\begin{cases}\) 5y = x^2 - 1 \\ x - y = 1 \(\end{cases}\)

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Textbook Question

Solve each system in Exercises 25–26. {x+32−y−12+z+24=32x−52+y+13−z4=−256x−34−y+12+z−32=−52\(\begin{cases}\[\frac{x + 3}{2}\) - \(\frac{y - 1}{2}\) + \(\frac{z + 2}{4}\) = \(\frac{3}{2}\) \(\frac{x - 5}{2}\) + \(\frac{y + 1}{3}\) - \(\frac{z}{4}\) = - \(\frac{25}{6}\) \(\frac{x - 3}{4}\) - \(\frac{y + 1}{2}\) + \(\frac{z - 3}{2}\) = - \(\frac{5}{2}\]\end{cases}\)

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