Question

Solve this system of equations algebraically: y x = 19 – x2 x y = 80 1. Isolate one variable in the system of equations. Y = –x2 – x 19 y = –x 80 2. Use substitution to create a one-variable equation. –x 80 = –x2 – x 19 3. Solve to determine the unknown variable in the equation. The system has real number solution(s).

Answer 1

System of equations helps to solve real-life problems. The system of equations will not have no solution.

What is a System of the equation?

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

The two of the system of equations given to us are,

$y+x=19-x^2$

$x+y = 80$

Now,

1. The first step is to isolate one variable in the system of equations,

$y=19-x^2-x$

$y=80-x$

2. The second step is to substitution to create a one-variable equation.

$80-x=19-x^2-x\\x^2-x+x=19-80\\x^2 = -61$

Now, since the value of x  is the negative square root. therefore, the system of equations will not have a real number of solutions.

If we plot the two equations on the graph, then the line of the system of equations will not intersect any point, therefore, the system of equations will have no solution.

Hence, the system of equations will not have no solution.

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