Question

A system of equations is shown below.
Equation A: 5x+9y=12
Equation B: 4x-3y=8
which method eliminates one of the variables

Answer 1

To eliminate one of the variables from the system of equations, you can use either the substitution method or the elimination method. Here, we will focus on the elimination method given the specific equations you provided:

**Equation A:** \(5x + 9y = 12\)
**Equation B:** \(4x - 3y = 8\)

To use the elimination method, we'll want to manipulate the equations so that we can eliminate one of the variables. Typically, this involves adjusting the coefficients of one of the variables in either equation. Here, let's eliminate \(y\).

1. **Multiply Equation B by 3** to make the coefficients of \(y\) in both equations match:
\[
3(4x - 3y) = 3(8) \implies 12x - 9y = 24
\]

So our new equations are:
- **Equation A:** \(5x + 9y = 12\)
- **Modified Equation B:** \(12x - 9y = 24\)

2. **Now, add the two equations** together to eliminate \(y\):
\[
(5x + 9y) + (12x - 9y) = 12 + 24
\]
\[
17x = 36
\]

Now, you can solve for \(x\).

Once you have \(x\), you can substitute it back into either original equation to solve for \(y\).

In summary, the elimination method as demonstrated here successfully eliminates the variable \(y\).