1 Answer

Manux · Answer 1 · 2023-07-12T12:36:23+0000

To find the system that has the given solution, replace those values on the equations and see if they are true.

For example, for the first system, replace each x by -2 and each y by 6 and see if the equations are true:

$\begin{gathered} y=2x+10 \\ 6=2(-2)+10 \\ 6=-4+10 \\ 6=6 \\ y=3x-6 \\ 6=3\mleft(-2\mright)-6 \\ 6=-6-6 \\ 6\\e-12 \end{gathered}$

The first system does not have that solution.

For the second system, do the same procedure:

$\begin{gathered} x+2y=10 \\ -2+2(6)=10 \\ -2+12=10 \\ 10=10 \\ -4x-y=2 \\ -4(-2)-6=2 \\ 8-6=2 \\ 2=2 \end{gathered}$

According to this, the second system has the given solution. It means that the correct answer is b.

To solve a system by elimination method, the first step is to multiply each equation by the coefficient of one of the variables of the other equation. If both coefficients have the same sign, change one of them.

For example:

In this case, we are going to use 5 and 4, which are the coefficiens of x in the first and second equation respectively. We need to multiply the first equation by 4 and the second one by 5, but as both coefficients have the same signs, one of them needs to be negative, then instead of 5 we are going to multiply by -5.

Now, add the resulting expressions:

Solve the resulting equation for y:

y has a value of -2. Then, you can use this value and one of the original equations to find x:

x has a value of 1. It means that the solution for this system is (1, -2)