Question

Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $\frac{x}{3}+\frac{y}{4}=1$ $2 x-3 y=12$

Name: Problem 22, Chapter 2: Intermediate Algebra for College Students
Uploaded: 2020-05-17T01:02:28-08:00
Duration: 1 min 21 s
Channel: Dale Sanford
Description: Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. (x)/(3)+(y)/(4)=1 2 x-3 y=12

   Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $\frac{x}{3}+\frac{y}{4}=1$
$2 x-3 y=12$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 2, Problem 22

Instant Answer

Solved by Expert Dale Sanford

05/17/2020

Step 1

For the first equation, $\frac{x}{3}+\frac{y}{4}=1$, we can solve for $y$ as follows: $\frac{y}{4} = 1 - \frac{x}{3}$ $y = 4\left(1 - \frac{x}{3}\right)$ $y = 4 - \frac{4x}{3}$ So, the first equation in slope-intercept form is $y = -\frac{4}{3}x + 4$. For Show more…

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Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. $\frac{x}{3}+\frac{y}{4}=1$ $2 x-3 y=12$

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Key Concepts

Slope-Intercept Form

This is a way to write the equation of a straight line so that the slope and the y-intercept are immediately clear. The general format is y = mx + b, where m represents the slope of the line and b represents the point where the line crosses the y-axis.

System of Linear Equations

A system of linear equations consists of two or more equations that share the same variables. The solution to the system is the set of values that satisfies all the equations simultaneously, representing the point(s) where the lines intersect on a coordinate plane.

Solution Types in Linear Systems

Systems of linear equations can have exactly one solution (if the lines intersect at one point), no solution (if the lines are parallel and never intersect), or an infinite number of solutions (if the lines are coincident, meaning they are the same line). Determining the type of solution typically involves comparing the slopes and intercepts of the lines.

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