Question

Determine the solution to each system of equations by substitution. $\frac{1}{2} x-\frac{1}{3} y=2$ $\frac{1}{4} x+\frac{2}{3} y=6$

Name: Problem 49, Chapter 4: Intermediate Algebra for College Students
Uploaded: 2022-02-10T18:02:20-08:00
Duration: 2 min 30 s
Channel: Rylie Howey
Description: Determine the solution to each system of equations by substitution. (1)/(2) x-(1)/(3) y=2 (1)/(4) x+(2)/(3) y=6

   Determine the solution to each system of equations by substitution. $\frac{1}{2} x-\frac{1}{3} y=2$
$\frac{1}{4} x+\frac{2}{3} y=6$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 4, Problem 49

Instant Answer

Solved by Expert Rylie Howey

02/10/2022

Step 1

Let's solve the first equation for x: $\frac{1}{2}x = 2 + \frac{1}{3}y$ Multiply both sides by 2 to get rid of the fraction: $x = 4 + \frac{2}{3}y$ Show more…

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Determine the solution to each system of equations by substitution. $\frac{1}{2} x-\frac{1}{3} y=2$ $\frac{1}{4} x+\frac{2}{3} y=6$

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Key Concepts

Working with Fractional Coefficients

When equations include fractions, it often helps to eliminate the fractions by multiplying both sides of the equation by a common denominator. This step simplifies the arithmetic and reduces the likelihood of algebraic errors during the solution process.

System of Linear Equations

A set of two or more equations involving the same set of variables where the goal is to find numbers that satisfy all equations simultaneously. In many cases, these systems represent intersecting lines or planes, and the solution corresponds to the intersection point(s).

Substitution Method

A method for solving a system of equations where one equation is solved for one variable in terms of the others and then substituted into the other equation(s). This reduces the system to fewer equations with fewer variables, simplifying the solving process.

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