solving with elimination practice

Answer 1

To solve a system of equations using the elimination method, follow these steps:

Step 1: Write down the two equations in the system.

Step 2: Choose a variable to eliminate. Look for a variable that will cancel out when you add or subtract the two equations.

Step 3: Multiply one or both equations by a constant if necessary to make the coefficients of that variable the same.

Step 4: Add or subtract the two equations to eliminate the chosen variable.

Step 5: Solve the resulting equation for the remaining variable.

Step 6: Substitute the value of the remaining variable back into one of the original equations to find the value of the eliminated variable.

Let's try an example:

1) 2x + 3y = 11
2) 3x - 2y = 2

Step 2: We can eliminate the variable y by adding the two equations together.

Step 3: We need to make the coefficient of y the same in both equations. We can do this by multiplying equation (1) by 2 and equation (2) by 3.

(2) 4x + 6y = 22
(3) 9x - 6y = 6

Step 4: Add equations (2) and (3) together:

4x + 6y + 9x - 6y = 22 + 6
13x = 28
x = 28/13

Step 5: Substitute x back into one of the original equations. Let's use equation (1):

2(28/13) + 3y = 11
56/13 + 3y = 11
3y = 143/13
y = 143/39

Therefore, the solution to the system of equations is x = 28/13 and y = 143/39.