Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
minus, 3, x, plus, 4, y, equals, minus, 50
−3x+4y=
−50
3, x, plus, 3, y, equals, minus, 6
3x+3y=
−6

Answer 1

To eliminate a variable from the given system of equations, you can choose to manipulate one or both of the equations so that when they are added or subtracted, one of the variables cancels out.

The two equations you provided are:

1. \(-3x + 4y = -50\) (Equation 1)
2. \(3x + 3y = -6\) (Equation 2)

**Step 1: Choose a variable to eliminate.**

Let's choose to eliminate \(x\). To do this, notice that you can multiply Equation 2 by 1 (in this case, it will not change the equation at the moment) to match the coefficient of \(x\) in Equation 1, or simply add the two equations as they are to see if they can cancel \(x\). However, to make it easier, we can multiply Equation 2 by \(-1\) to use its opposite sign:

\[
- (3x + 3y) = -(-6) \rightarrow -3x - 3y = 6
\]

Now you have:

1. \(-3x + 4y = -50\)
2. \(-3x - 3y = 6\)

**Step 2: Subtract Equation 2 from Equation 1.**

Now, you can subtract Equation 2 from Equation 1 to eliminate \(x\):

\[
(-3x + 4y) - (-3x - 3y) = -50 - 6
\]

This will eliminate the \(x\) term:

\[
4y + 3y = -50 - 6
\]
\[
7y = -56
\]

Now you can solve for \(y\).

So, the initial step you would take is to multiply the second equation by -1 to facilitate elimination of \(x\). Alternatively, you could manipulate the first equation to make elimination easier if preferred.

In summary, the first step to eliminate \(x\) could involve either rearranging or multiplying the equations to make the coefficients match for \(x\).