Solve 3a - b + 2c = 1; - 2a + 5c = 5; 4a + 3b - c = 2 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3a-b+2c=1; -2a+5c=5; 4a+3b-c=2$$

Solve for a, b, c

$a=0$
$b=1$
$c=1$

Short Steps Using Substitution

Solve $3a-b+2c=1$ for $b$.

$$b=3a+2c-1$$

Substitute $3a+2c-1$ for $b$ in the equation $4a+3b-c=2$.

$$4a+3\left(3a+2c-1\right)-c=2$$

Solve the second equation for $a$ and the third equation for $c$.

$$a=-\frac{5}{2}+\frac{5}{2}c$$ $$c=-\frac{13}{5}a+1$$

Substitute $-\frac{5}{2}+\frac{5}{2}c$ for $a$ in the equation $c=-\frac{13}{5}a+1$.

$$c=-\frac{13}{5}\left(-\frac{5}{2}+\frac{5}{2}c\right)+1$$

Solve $c=-\frac{13}{5}\left(-\frac{5}{2}+\frac{5}{2}c\right)+1$ for $c$.

$$c=1$$

Substitute $1$ for $c$ in the equation $a=-\frac{5}{2}+\frac{5}{2}c$.

$$a=-\frac{5}{2}+\frac{5}{2}\times 1$$

Calculate $a$ from $a=-\frac{5}{2}+\frac{5}{2}\times 1$.

$$a=0$$

Substitute $0$ for $a$ and $1$ for $c$ in the equation $b=3a+2c-1$.

$$b=3\times 0+2\times 1-1$$

Calculate $b$ from $b=3\times 0+2\times 1-1$.

$$b=1$$

The system is now solved.

$$a=0$$ $$b=1$$ $$c=1$$