Final answer:
The system of equations is solved by subtracting one equation from the other to eliminate the y terms, leaving 2x = -4. Solving for x gives x = -2. Substituting x into one of the original equations and solving for y gives y = 9.
Step-by-step explanation:
To solve the system of equations 7x+2y=4 and 9x+2y=0 by combining the equations, we can use the method of elimination. Since the coefficients of y are the same in both equations, we can directly subtract one equation from the other to eliminate the y terms.
- Equation 1: 7x + 2y = 4
- Equation 2: 9x + 2y = 0
Subtract equation 1 from equation 2:
(9x + 2y) - (7x + 2y) = (0) - (4)
This simplifies to:
9x - 7x + 2y - 2y = -4
Which further simplifies to:
2x = -4
Now divide both sides by 2 to solve for x:
x = -4/2
x = -2
With x found, we can substitute it into either of the original equations to find y. Using the first equation:
7(-2) + 2y = 4
-14 + 2y = 4
Add 14 to both sides:
2y = 4 + 14
2y = 18
Now divide by 2:
y = 18/2
y = 9
Thus, the solution to the system of equations is x = -2 and y = 9.