Question

What is the solution of the linear-quadratic system of equations y=x^2 5x-3 x-y=2?

Answer 1

we have

$y=x^2+ 5x-3$ -------> equation $1$

$x-y=2$ -------> equation $2$

we know that

The system solution will be the points of intersection of both graphs

Using a graph tool

see the attached figure

the solution are the points

$(-4.2,6.2)\ and\ (0.2,-1.8)$

Answer 2

The solution of the linear-quadratic system of equations $y = {x^2} + 5x - 3$ and $x - y = 2$ are $\left( { - 4.23, - 6.23} \right)$ and $\left( {0.23, - 1.77} \right).$

Further explanation:

Given:

The linear equation is x - y = 2.

The quadratic equation is y = {x^2} + 5x – 3.

Explanation:

The given linear equation is x - y = 2.

The given quadratic equation is y = {x^2} + 5x – 3.

Solve the linear equation x - y = 2.

$\begin{aligned}x - y&=2\\x&= 2 + y\\x - 2&= y\\\end{aligned}$

Substitute x-2 for y in quadratic equation.

$\begin{aligned}x - 2&= {x^2} + 5x - 3\\0&= {x^2} + 5x - 3 - x + 2\\0&= {x^2} + 4x - 1\\\end{aligned}$

Solve the quadratic equation ${x^2} + 4x - 1 = 0.$

Now find the value of discriminant.

$\begin{aligned}D&= {b^2} - 4ac\\&= {\left( 4\right)^2}- 4\times 1\times\left({ - 1}\right)\\&= 16 + 4\\&= 20\\\end{aligned}$

The value of can be obtained as follows,

$\begin{aligned}x&=\frac{{ - b \pm \sqrt D }}{{2a}}\hfill\\x&=\frac{{ - 4 \pm \sqrt {20} }}{{2 \times 1}}\hfill\\\end{aligned}$

The first value of x can be calculated as follows,

$\begin{aligned}x&=\frac{{- 4 -\sqrt {20} }}{2}\\&= \frac{{ - 4 - 4.46}}{2}\\&= 4.23\\\end{aligned}$

The value of y can be obtained as follows,

$\begin{aligned}y&= x - 2\\&= - 4.23 - 2\\&=- 6.23\\\end{aligned}$

The second value of x can be obtained as follows,

$\begin{aligned}&=\frac{{ - 4 + \sqrt {20} }}{2}\\&=\frac{{ - 4 + 4.46}}{2}\\&=\frac{{0.46}}{2}\\&= 0.23 \\\end{aligned}$

The value of y can be obtained as follows,

$\begin{aligned}y&= 0.23 - 2\\&=- 1.77\\\end{aligned}$

Hence, the solution of the linear-quadratic system of equations $y = {x^2} + 5x - 3$ and $x - y = 2$ are $\left( { - 4.23, - 6.23}\right)$ and $\left( {0.23, - 1.77}\right).$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equation

Keywords: polynomial, solution, linear equation, quadratic equation, system of equations, solution of the equations.