Final answer:
To solve the system of equations using elimination, we first matched the y coefficients and subtracted one equation from the other to find x = 2. Substituting x back into one of the original equations gave us y = 5. Checking these values in both original equations confirms the solution is correct.
Step-by-step explanation:
To solve the system of equations using elimination, we want to find a way to eliminate one of the variables by combining the two equations. We have the equations -2x + 2y = 6 and 7x + 4y = 34.
First, let's try to eliminate the variable y. To do this, we can multiply the first equation by 2 so that the coefficients in front of y in both equations match. Multiplying the first equation by 2 gives us:
-4x + 4y = 12
Now we have:
- Equation 1: -4x + 4y = 12
- Equation 2: 7x + 4y = 34
Next, we subtract Equation 1 from Equation 2 to eliminate y:
(7x + 4y) - (-4x + 4y) = 34 - 12
This simplifies to:
11x = 22
Divide both sides by 11:
x = 2
Now that we have the value for x, we can substitute it back into one of the original equations to solve for y. Using the first equation -2x + 2y = 6:
-2(2) + 2y = 6
-4 + 2y = 6
Add 4 to both sides:
2y = 10
Divide both sides by 2:
y = 5
Therefore, the solution to the system of equations is x = 2 and y = 5. It is always a good idea to check the solution by plugging the values back into the original equations to ensure they satisfy both.