To solve the system of equations, we have:
- \( 2x + 8y = 8 \)
- \( 2x - 4y = -16 \)
We can solve this system using either substitution or elimination. Here, let's use elimination.
First, we can simplify both equations if needed.
Starting with the first equation:
- \( 2x + 8y = 8 \) can be divided by 2: \[ x + 4y = 4 \]
Now the first equation is: \[ x + 4y = 4 \tag{1} \]
Now simplify the second equation: 2. \( 2x - 4y = -16 \) can also be divided by 2: \[ x - 2y = -8 \]
Now the second equation is: \[ x - 2y = -8 \tag{2} \]
Now we will subtract equation (1) from equation (2) to eliminate \(x\): \[ (x - 2y) - (x + 4y) = -8 - 4 \] This simplifies to: \[ -2y - 4y = -12 \] Combine like terms: \[ -6y = -12 \]
Now, divide by -6: \[ y = 2 \]
Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use equation (1): \[ x + 4(2) = 4 \] This simplifies to: \[ x + 8 = 4 \] Subtracting 8 from both sides gives: \[ x = 4 - 8 \] \[ x = -4 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-4, 2) \]
So the answer is: \[ (-4, 2) \]
1 answer