Beyonce is solving a system of equations:

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

Answer:

Beyonce will get the same result.

Step-by-step explanation:

The given system is

2x-3y=-2

and 4

x+y=24

This system contains two lines that are not parallel to each other therefore the solution x=5, y=4 is unique.

It doesn't matter which method he used or which variable he eliminated first.

The solution will still be the same.

If the system of two equations with has no solution, the Beyonce will not get a solution in the first place, but the fact that the system has no solution remains the same even if Beyonce uses a different method.

If there are infinite solutions, Beyonce might get different solutions using a different method, but the fact that the system has infinite solution remains the same.

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Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$