Ch. 5 - Systems of Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Problema 23

Capitolo 6, Problema 23

In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25

Guida verificata passo dopo passo

Step 1: Multiply the first equation by 4 to align the coefficients of x.

Step 2: Add the modified first equation to the second equation to eliminate x.

Step 3: Solve the resulting equation for y.

Step 4: Substitute the value of y back into the original first equation.

Step 5: Solve for x.

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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.

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Introduction to Systems of Linear Equations

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 method requires manipulating the equations so that the coefficients of one variable are opposites, allowing for straightforward elimination.

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How to Multiply Equations in Elimination Method

Solving for Variables

After eliminating one variable, the resulting single-variable equation can be solved using basic algebraic techniques. Substituting this solution back into one of the original equations allows for finding the value of the other variable, completing the solution to the system.

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Equations with Two Variables

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