Linear Equations Calculator

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Example

Created on 2024-06-20Asked by Eleanor Nelson (Solvelet student)

Solve the system of linear equations:

\begin{cases} 2x + 3y = 5 \\ 4x - y = 11 \end{cases}

Solution

To solve the system of linear equations:

\begin{cases} 2x + 3y = 5 \\ 4x - y = 11 \end{cases}

we use the substitution or elimination method. Here, we use the elimination method. First, multiply the second equation by 3 to align the coefficients of

y

3(4x - y) = 3(11)

12x - 3y = 33

Now, add this equation to the first equation to eliminate

y

(2x + 3y) + (12x - 3y) = 5 + 33

14x = 38

Solve for

x

x = \frac{38}{14} = \frac{19}{7}

Substitute

x = \frac{19}{7}

back into the first equation to find

y

2\left( \frac{19}{7} \right) + 3y = 5

\frac{38}{7} + 3y = 5

3y = 5 - \frac{38}{7} = \frac{35}{7} - \frac{38}{7} = -\frac{3}{7}

y = -\frac{1}{7}

Therefore, the solution to the system is:

\left( \frac{19}{7}, -\frac{1}{7} \right)

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Alexander Johnson on Solvelet

1. Solve the linear equation

2x + 3 = 7

.2. Graph the line represented by the equation

y = 2x - 3

DefinitionLinear equations are the algebraic equations consisting of either a constant or a single variable, or a constant and the product of a single variable. This could be written in the form of ax+b=0, where a and b are constants. The graph of a line represents a solution to linear equation. - 2x+3=7 - This is a type of linear equation - Solve to get x=2.

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