Question

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

Answer 1

The best method is : is elimination by substitution

Step-by-step 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=(-5-3y)/(4)\text{ x}=(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=(-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=(-5-3y)/(4) \\ x=(-5-3(1))/(4) \\ x=(-5-3)/(4) \\ x=(-8)/(4) \\ x=-2 \\ 2.\text{ x}=(6-2y)/(-2) \\ x=(6-2(1))/(-2) \\ x=(6-2)/(-2) \\ x=(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.