Skip to main content
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 11
Chapter 6, Problem 11

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0
Two linear equations for a system: 5x + 2y = 0 and x - 3y = 0.

Verified step by step guidance
1
Start with the given system of equations: 5x+2y=0x-3y=0.
Solve one of the equations for one variable in terms of the other. For example, from the second equation x - 3y = 0, solve for x: x = 3y.
Substitute the expression for x from step 2 into the first equation: replace x with 3y in 5x + 2y = 0 to get 5(3y) + 2y = 0.
Simplify the resulting equation and solve for y: 15y + 2y = 0 which simplifies to 17y = 0, then solve for y.
Use the value of y found in step 4 and substitute it back into the expression for x from step 2 to find the value of x.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

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 variable values that satisfy all equations simultaneously. Understanding how to interpret and represent these systems is fundamental to solving them.
Recommended video:
Guided course
4:27
Introduction to Systems of Linear Equations

Substitution Method

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. This reduces the system to a single equation with one variable, making it easier to solve step-by-step.
Recommended video:
04:03
Choosing a Method to Solve Quadratics

Solving Linear Equations

Solving linear equations requires isolating the variable using algebraic operations such as addition, subtraction, multiplication, and division. Mastery of these operations is essential to find the exact values of variables in the system.
Recommended video:
04:02
Solving Linear Equations with Fractions
Related Practice
Textbook Question

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 1/x(x-1)

674
views
Textbook Question

Write the partial fraction decomposition of each rational expression. (3x +50)/(x -9)(x +2)

599
views
Textbook Question

Solve each system in Exercises 5–18. {2x−4y+3z=17x+2y−z=04x−y−z=6\(\begin{cases}\)2x - 4y + 3z = 17 \(\x\) + 2y - z = 0 \\4x - y - z = 6\(\end{cases}\)

648
views
Textbook Question

Graph each inequality. x≤−3

691
views
Textbook Question

In Exercises 1–18, solve each system by the substitution method. {y2=x2−92y=x−3\(\begin{cases}\)y^2 = x^2 - 9 \\2y = x - 3\(\end{cases}\)

646
views
Textbook Question

Write the partial fraction decomposition of each rational expression. x/(x-2)(x-3)

702
views