Skip to main content
Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 25
Chapter 6, Problem 25

Solve each system by elimination. In systems with fractions, first clear denominators.
6x + 7y + 2 = 0
7x - 6y - 26 = 0

Verified step by step guidance
1
Rewrite each equation to isolate the constant term on the right side. For the first equation, subtract 2 from both sides to get \(6x + 7y = -2\). For the second equation, add 26 to both sides to get \(7x - 6y = 26\).
Set up the system of equations for elimination: \(6x + 7y = -2\) \(7x - 6y = 26\)
To eliminate one variable, find a common multiple for the coefficients of either \(x\) or \(y\). For example, multiply the first equation by 6 and the second equation by 7 to align the coefficients of \(y\): \(6(6x + 7y) = 6(-2) \Rightarrow 36x + 42y = -12\) \(7(7x - 6y) = 7(26) \Rightarrow 49x - 42y = 182\)
Add the two new equations to eliminate \(y\): \((36x + 42y) + (49x - 42y) = -12 + 182\) This simplifies to \(85x = 170\).
Solve for \(x\) by dividing both sides by 85, then substitute the value of \(x\) back into one of the original equations to solve for \(y\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

Key Concepts

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

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The goal is to find values for the variables that satisfy all equations simultaneously. Understanding how to interpret and set up these systems is essential for solving them.
Recommended video:
Guided course
4:27
Introduction to Systems of Linear Equations

Elimination Method

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable. This technique often requires multiplying equations by constants to align coefficients before elimination.
Recommended video:
Guided course
6:04
How to Multiply Equations in Elimination Method

Clearing Fractions

When equations contain fractions, multiplying both sides by the least common denominator removes the fractions, simplifying calculations. Clearing denominators helps avoid errors and makes the elimination process more straightforward.
Recommended video:
Guided course
05:45
Radical Expressions with Fractions
Related Practice
Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (3x - 2)/((x + 4)(3x2 + 1))

709
views
Textbook Question

Find the inverse, if it exists, for each matrix. [233143134]\(\left\)[ \(\begin{matrix}\) 2 & 3 & 3 \\1 & 4 & 3 \\1 & 3 & 4 \(\end{matrix}\) \(\right\)]

629
views
Textbook Question

Solve each system, using the method indicated.

5x + 2y = -10

3x - 5y = -6 (Gauss-Jordan)

800
views
Textbook Question

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

6x - 3y - 4 = 0

3x + 6y - 7= 0

1231
views
Textbook Question

Graph each inequality. x2 + (y + 3)2 ≤ 16

506
views
Textbook Question

Evaluate each determinant.

∣1021−143−3810∣\(\left\)| \(\begin{matrix}\) 10 & 2 & 1 \\ -1 & 4 & 3 \\ -3 & 8 & 10 \(\end{matrix}\) \(\right\)|

745
views