Question

Solve by substitution. $$ 17 x-y=1214 x+12 y=2 $$

   Solve by substitution.
$$
17 x-y=1214 x+12 y=2
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 4, Problem 38

Instant Answer

Solved by Expert James Kiss

01/27/2022

Step 1

We subtract $\frac{1}{7}x$ from both sides and add $y$ to both sides to get $y = \frac{1}{7}x - \frac{1}{2}$. Show more…

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Solve by substitution. $$ 17 x-y=1214 x+12 y=2 $$

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Key Concepts

Systems of Linear Equations

A system of linear equations is a collection of two or more linear equations that share the same set of variables. The goal is to find values for these variables that satisfy every equation in the system concurrently. Such systems form the foundation for understanding relationships between variables in algebra and are widely applicable in various fields of science and engineering.

Substitution Method

The substitution method is a strategy for solving systems of equations by isolating one variable in one equation and substituting that expression into the other equation(s). This reduces the number of equations and variables, eventually allowing for the solution of the original system. It is particularly useful when one equation can be easily rearranged to solve for one variable, simplifying the process of finding the values of all variables involved.

Isolation of Variables

Isolation of variables is the process of rearranging an equation so that one variable is expressed solely in terms of the other variables and constants. This technique is essential in the substitution method because it helps to eliminate one variable from the system, making it easier to solve the remaining equation(s). It is a fundamental tool in algebra for managing and solving equations efficiently.

Verification of Solutions

Verification of solutions involves substituting the obtained values of the variables back into the original equations to ensure that they satisfy all the given conditions. This step confirms the accuracy of the solution and is a critical part of solving any system of equations, as it helps to catch any errors made during the manipulation or calculation process.

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