Question

you are given the system of equations
16x-10y=10
-8x-6y=6
to solve this by elimination which of the following is one possible first step you could take

Answer 1

To solve the system of equations by elimination, a good first step is to manipulate the equations to get the coefficients of one of the variables to be opposites so that they can be eliminated when the equations are added or subtracted.

Here are the original equations:

1. \( 16x - 10y = 10 \) (Equation 1)
2. \( -8x - 6y = 6 \) (Equation 2)

One possible first step is to multiply the second equation by 2, which will allow us to align the coefficients of \( x \) in both equations for elimination.

Multiplying the second equation by 2:

\[
2(-8x - 6y) = 2(6)
\]

This gives us:

\[
-16x - 12y = 12 \quad \text{(Equation 3)}
\]

Now, the system looks like this:

1. \( 16x - 10y = 10 \) (Equation 1)
2. \( -16x - 12y = 12 \) (Equation 3)

Now you can add Equation 1 and Equation 3 together to eliminate \( x \):

\[
(16x - 10y) + (-16x - 12y) = 10 + 12
\]
\[
-22y = 22
\]

This step enables you to solve for one of the variables. So, one possible first step you could take is to multiply the second equation by 2.