Systems of Equations Calculator

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Example

Created on 2024-06-20Asked by Avery Williams (Solvelet student)

Solve the system of equations:

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

Solution

To solve the system of equations:

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

1. **Solve the second equation for

y

:**

y = 4x - 5.

2. **Substitute

y

in the first equation:**

2x + 3(4x - 5) = 6 \implies 2x + 12x - 15 = 6 \implies 14x = 21 \implies x = \frac{21}{14} = \frac{3}{2}.

3. **Solve for

y

:**

y = 4 \left(\frac{3}{2}\right) - 5 = 6 - 5 = 1.

4. **Result:** The solution is

x = \frac{3}{2}

y = 1

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Sebastian Taylor on Solvelet

1. Solve the system of equations

3x + 2y = 7

x - 4y = -5

.2. Find the solution to the system of equations

2x + y = 4

x - y = 1

DefinitionSystems of equations mean to find the common solution for multiple equations with multiple variables. Which can be linear or non-linear systems. Case: Solving the System: x+y=5; 2x−y=1 The solution is x=2 and y=3

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