Question

5x+3y=4
-2x-8y=6
Which strategy can you use to eliminate a variable

Answer 1

To eliminate a variable from the system of equations given by:

1. \( 5x + 3y = 4 \)
2. \( -2x - 8y = 6 \)

you can use the method of **multiplication** to make the coefficients of one of the variables the same (or opposites) in both equations.

**Here's a step-by-step process:**

1. **Identify a Variable to Eliminate:** We can choose to eliminate \(x\) or \(y\). Here, we'll eliminate \(x\).

2. **Make the Coefficients of \(x\) the Same:** You can multiply the first equation by \(2\) so that the coefficient of \(x\) in both equations will match.

\[
2(5x + 3y) = 2(4) \implies 10x + 6y = 8
\]

Now our system of equations looks like:

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

3. **Multiply the Second Equation:** To eliminate \(x\), multiply the second equation by \(5\) so the coefficient of \(x\) also becomes \(10\).

\[
5(-2x - 8y) = 5(6) \implies -10x - 40y = 30
\]

Now the system is:

1. \( 10x + 6y = 8 \)
2. \( -10x - 40y = 30 \)

4. **Add the Two Equations Together:** When you add the modified equations together, the \(x\) terms will cancel out.

\[
(10x - 10x) + (6y - 40y) = 8 + 30
\]
This simplifies to:
\[
-34y = 38
\]

5. **Solve for \(y\):**

\[
y = -\frac{19}{17}
\]

6. **Substitute Back to Find \(x\):** You can now substitute the value of \(y\) back into either original equation to find \(x\).

Using this method, you will successfully eliminate one variable and solve for the remaining variable.