Question

a system of equations is shown below
equation a: 5x+9y=12
equation b: 4x-3y=8
which method elminates one of the variables?

Answer 1

To eliminate one of the variables in a system of equations, you can use either the substitution method or the elimination method.

In this case, the elimination method is likely the most straightforward since both equations can be manipulated to eliminate either variable.

To proceed with elimination, you can multiply each equation by a suitable number to make the coefficients of either \( y \) or \( x \) the same so that adding or subtracting the equations will eliminate that variable:

1. **To eliminate \( y \):**
- Multiply Equation a (5x + 9y = 12) by 3, resulting in:
\[ 15x + 27y = 36 \]
- Multiply Equation b (4x - 3y = 8) by 9, resulting in:
\[ 36x - 27y = 72 \]

Now you can add the two modified equations together. The \( y \) terms will cancel out because their coefficients are opposites (+27y and -27y).

2. **To eliminate \( x \):**
- Alternatively, if you wanted to eliminate \( x \), you could multiply Equation a by 4 and Equation b by 5:
\[ 20x + 36y = 48 \]
\[ 20x - 15y = 40 \]

Then, subtract the second modified equation from the first. The \( x \) terms will cancel out.

In summary, both the elimination of \( y \) and the elimination of \( x \) will work, depending on which variable you decide to eliminate first. The method is called "elimination" because it involves eliminating one of the variables by manipulating the equations.