Question

Use the elimination process to find the solution to the following system of equations. Include the solution (x, y) AND your explanation 5x + 4y = 8 -5x - 3y = 4

Answer 1

By using the elimination method, the x variable was cancelled, leading to finding the value of y, which was then substituted back into an equation to find x, resulting in the solution (x, y) = (-8, 12).

Step-by-step explanation:

To solve the system of equations 5x + 4y = 8 and -5x - 3y = 4 using the elimination method, we look to eliminate one of the variables by adding or subtracting the equations. When we add the two equations together, we eliminate the x variable, since 5x and -5x cancel each other out:

1. 5x + 4y = 8
2. -5x - 3y = 4
3. Add the two equations: (5x - 5x) + (4y - 3y) = 8 + 4
4. This simplifies to y = 12

Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

1. 5x + 4(12) = 8
2. 5x + 48 = 8
3. 5x = 8 - 48
4. 5x = -40
5. x = -8

We should always check our answer to ensure it's reasonable by substituting x and y back into the original equations. After checking, we confirm that the solution is correct:

• 5(-8) + 4(12) = 8
• -5(-8) - 3(12) = 4

Therefore, the solution to the system of equations is (x, y) = (-8, 12).