Two-variable linear equations Calculator

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Example

Created on 2024-06-20Asked by Owen Ramirez (Solvelet student)

Solve the system of linear equations:

\begin{cases} 2x + 3y = 6 \\ 4x - y = 5 \end{cases}

Solution

To solve the system of linear equations:

\begin{cases} 2x + 3y = 6 \\ 4x - y = 5 \end{cases}

1. **Multiply the second equation by 3 to align coefficients:**

4x - y = 5 \implies 12x - 3y = 15.

2. **Add the resulting equation to the first equation:**

(2x + 3y) + (12x - 3y) = 6 + 15 \implies 14x = 21 \implies x = \frac{21}{14} = \frac{3}{2}.

3. **Substitute

x = \frac{3}{2}

into the first equation:**

2\left(\frac{3}{2}\right) + 3y = 6 \implies 3 + 3y = 6 \implies 3y = 3 \implies y = 1.

4. **Result:** The solution to the system is

x = \frac{3}{2}

and

y = 1

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Benjamin Roberts on Solvelet

1. Solve the system of equations:

2x + 3y = 7

and

x - 4y = -5

.2. Determine the slope of the line passing through the points

(2, 3)

and

(4, 5)

DefinitionLinear Equations in One Variable are called as One-variable linear equations that are in form of ax+by=c where, a,b and c are some constant values. The solutions are the pairs (x,y) that satisfy the equation, usually graphed as a line in the xy-plane. E.g The equation 2x+3y=6 represents a straight line.These may be written in the format, ax+byc as well as ax+by

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