**y = x^2 + 3****y = x + 5**

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**question aims to solve the linear equation system**and calculate the variable’s values. In mathematics, a set of simultaneous equations, also known as a system of equations or equation systems, is a limited set of mathematics equations required by the exact solutions. The**mathematical system**is usually divided in the same way as single statistics, namely: **System of nonlinear equations****System of linear equations****System of the bilinear equation****System of differential equations****System of difference equation**

A system of **linear equations** is a defined **combination of one or more linear equations having the same variable**. In mathematics, **line programming theory** is a fundamental component of linear algebra, a term used in many parts of modern mathematics. **Computer algorithms** for finding solutions are an integral part of algebra in the number line and play an important role in engineering, physics, chemistry, computer science, and economics. A **non-line mathematical system** can usually be measured by a line system, a helpful method for modeling a **mathematical model** or comparing a computer system with a relatively complex one.

Generally, **mathematical coefficients are real or complex numbers,** and **solutions** are searched in a set of the same numbers. Still, the theory and algorithms apply to coefficients and solutions in any field. **Some ideas** have been made to find answers in an important domain, such as the ring of whole numbers or other algebraic structures; see the line number above the ring. Integer linear programming is a set of methods for finding the “best” number solution (if there are many). **Gröbner’s core theory provides** algorithms in which coefficients and anonymity are polynomials. And the **geometry of the tropics** is an example of line algebra in an unusual structure.

The **line system solution is the numerical value of the variables** $x_[{1}, x_{2}, …, x_{n}$ to satisfy each figure. The set of all possible solutions determines the solution set of the equations.

The line system can work in any of** three possible ways:**

–The system has **complete solutions**.

-The program has one **unique solution.**

-The system has **no solution.**

## Expert Answer

**Solving these two equations give us:**

\[y=x^{2}+3\]

\[y=x+5\]

\[x^{2}+3=x+5\]

\[x^{2}-x=5-3\]

\[x^{2}-x=2\]

\[x^{2}-x-2=0\]

\[x^{2}-2x-x-2=0\]

\[x(x-2)+1(x-2)=0\]

\[(x+1)(x-2)=0\]

\[x+1=0 \:or\: x-2=0\]

\[x=-1\: or \: x=2\]

\[x=-1,2\]

## Numerical Results

**Solving the system of two equations gives values** of $x=-1,2$.

## Example

**Solve the system of equations as shown below and show all work.**

$x+y=8$

$2x+y=13$

**Solution**

**Solving these two equations gives us:**

\[x+y=8\]

\[2x+y=13\]

\[y=8-x\]

\[y=13-2x\]

\[x^{2}+8=x-3\]

\[8-x=13-2x\]

\[-2x+x=8-13\]

\[-x=-5\]

\[x=5\]

\[y=8-x\]

\[y=8-5\]

\[y=3\]

\[x=5\: or \:y=3\]

\[x=5 \:and\: y=3\]

** ****Solving the system of two equations** gives the value of $x=5 \:and \:y=3$.