Answer: (8/7, 4/3).
Explanation:
To use the elimination method to find the solution set of the equation, we need to have two equations in the same form, either both in standard form or both in slope-intercept form. Let's assume we have two equations, Equation 1 and Equation 2.
1. Write both equations in the same form:
Let's say Equation 1 is in the form "ax + by = c" and Equation 2 is in the form "dx + ey = f".
If the equations are not in the same form, rearrange them so they are. For example, convert Equation 2 to the form "ax + by = c".
2. Multiply one or both equations by a constant to create opposite coefficients for one of the variables:
Look at the coefficients of either x or y in Equation 1 and Equation 2. Multiply one or both equations by a constant so that the coefficients of the variable you choose have opposite signs.
3. Add the equations together:
Add Equation 1 and Equation 2 together to eliminate one of the variables. This will result in a new equation with only one variable.
4. Solve for the remaining variable:
Solve the new equation for the remaining variable. This will give you a value for that variable.
5. Substitute the value back into one of the original equations:
Take the value you found for the remaining variable and substitute it back into one of the original equations. This will give you the corresponding value for the other variable.
6. Write the solution set:
Write the solution set as an ordered pair (x, y) with the values you found for both variables.
Example:
Let's say we have the following two equations:
Equation 1: 3x + 2y = 8
Equation 2: 2x - 4y = -10
1. Both equations are already in standard form.
2. Multiply Equation 2 by 2 to create opposite coefficients for x:
Equation 2 becomes: 4x - 8y = -20
3. Add the equations together:
(3x + 2y) + (4x - 8y) = 8 + (-20)
Simplifying, we get: 7x - 6y = -12
4. Solve for x:
Let's assume x = t (a variable).
7t - 6y = -12
7t = 6y - 12
t = (6y - 12) / 7
5. Substitute t back into Equation 1:
3(t) + 2y = 8
3((6y - 12) / 7) + 2y = 8
Simplifying, we get: y = 4/3
6. Write the solution set:
The solution set is (t, y) or (6(4/3) - 12/7, 4/3).
Simplifying, we get: (8/7, 4/3).
Please note that this is just one example, and the specific steps may vary depending on the equations provided. Remember to always double-check your work and ensure that your solution satisfies both equations.