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Example

Created on 2024-06-20Asked by William Wilson (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. **Multiply the second equation by 3 to align the coefficients of

y

:**

12x - 3y = 15.

2. **Add the modified second equation to the first equation:**

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

3. **Substitute

x

back into the first equation:**

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

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

x = \frac{3}{2}

y = 1

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Ava Anderson on Solvelet

1. Develop a strategy to solve a system of linear equations with three variables using Gaussian elimination.2. Apply the bisection method to find the root of the equation

f(x) = x^3 - 5x^2 + 4x + 3

in the interval

[1, 3]

DefinitionMathematical solution methods and techniques of equations and problems are methods that solve equations in analytical, numerical and graphical categories. For example, solving the quadratic equation ax2+bx+c=0 using the quadratic formula x=2a−b±b2−4ac.

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