Final answer:
The correct first step in solving a system of equations by elimination is to identify a variable that can be eliminated when the equations are added together. The coefficients of the variable should be equal but have opposite signs. Multiplying one or both equations by appropriate constants can help achieve this.
Step-by-step explanation:
The correct first step to solve a system of equations by elimination is to identify a variable that can be eliminated when the equations are added together. This is done by ensuring that the coefficients of one of the variables in both equations are equal but have opposite signs. Once the variable is identified, the two equations are added together, resulting in a new equation with one variable eliminated.
For example, let's say we have the following system of equations:
Equation 1: 2x + 3y = 5
Equation 2: 3x - 2y = 4
We can see that if we multiply Equation 1 by 3 and Equation 2 by 2, the coefficients of y will be equal but have opposite signs. So, the correct first step would be to add the two equations together:
(3 * Equation 1) + (2 * Equation 2)
6x + 9y + 6x - 4y = 15 + 8
12x + 5y = 23
Learn more about Solving a system of equations by elimination