Question

what is the best method to solve 4x+3y=-5 -2x+2y=6 and why?

Answer 1

ANSWER:

The best method is : is elimination by substitution

EXPLANATION:

First we must eliminate one of the variables in both equations, that is, x, to find y, then we must substitute the value of y in one of the equations to find the value of x

$\begin{gathered} 1.4x+3y=-5 \\ 4x=-5-3y \\ 2.-2x+2y=6 \\ -2x=6-2y \\ Now\text{ }we\text{ find y:} \\ x=\frac{-5-3y}{4}\text{ x}=\frac{6-2y}{-2} \\ \text{Now }we\text{ equate }both\text{ equations:} \\ 4(6)(-2y)=-2(-5)(-3y) \\ 24-8y=10+6y \\ -8y-6y=10-24 \\ -14y=-14 \\ y=\frac{-14}{-14} \\ y=1 \end{gathered}$

Now we must replace that value in both equations to have the value of x.

(The value of x must be the same for the two equations ;If the value of x is the same that means that the value of y was correctly found.,)

$\begin{gathered} 1.x=\frac{-5-3y}{4} \\ x=\frac{-5-3(1)}{4} \\ x=\frac{-5-3}{4} \\ x=\frac{-8}{4} \\ x=-2 \\ 2.\text{ x}=\frac{6-2y}{-2} \\ x=\frac{6-2(1)}{-2} \\ x=\frac{6-2}{-2} \\ x=\frac{4}{-2} \\ x=-2 \end{gathered}$

To verify that the system is well solved, those values ​​found must be replaced in the original equation and it must give us the value of the equation.

1.EQUATION:

$\begin{gathered} 4x+3y=-5 \\ 4(-2)+3(1)=-5 \end{gathered}$

We can see by replacing the values ​​found for x and for y that it gives us -5 which shows that the system was correctly developed.

2.EQUATION:

$\begin{gathered} -2x+2y=6 \\ -2(-2)+2(1)=6 \end{gathered}$

Again we replace the found values ​​of x and y in the second equation and it gives us the answer correctly, which confirms that the system was perfectly developed.