Question

To solve the linear system of equations using the addition method (also known as the elimination method), we will first write down the equations:
x−y=4 (Equation 1)
x+2y=4 (Equation 2)
The goal of the addition method is to eliminate one of the variables by adding or subtracting the equations.
Step 1: Align the equations
We have:
Equation 1: x−y=4
Equation 2: x+2y=4
Step 2: Make the coefficients of one variable the same
In order to eliminate x, we can subtract Equation 1 from Equation 2.
Rearranging Equation 1:
x=y+4
Now substitute x in Equation 2 using the value from Equation 1:(y+4)+2y=4
Step 3: Simplify and solve for y
Combining like terms:y+4+2y=43y+4=4Subtract 4 from both sides:3y=0Now, divide by 3:y=0
Step 4: Substitute y back into one of the original equations to solve for x
Now that we know y=0, substitute this value into Equation 1 to find x:x−0=4x=4
Conclusion
The solution to the system of equations is:

can you make this way less advaned and use less words

Answer 1

Sure! Here's a simpler version:

We have two equations:

1. \( x - y = 4 \)
2. \( x + 2y = 4 \)

**Step 1:** Align the equations.

**Step 2:** Let's eliminate \( x \).
From Equation 1, we can express \( x \):
\( x = y + 4 \)

**Step 3:** Substitute \( x \) in Equation 2:
\( (y + 4) + 2y = 4 \)
Combine like terms:
\( 3y + 4 = 4 \)
Subtract 4 from both sides:
\( 3y = 0 \)
Now, divide by 3:
\( y = 0 \)

**Step 4:** Substitute \( y \) back into Equation 1 to find \( x \):
\( x - 0 = 4 \)
So, \( x = 4 \)

**Conclusion:**
The solution is \( x = 4 \) and \( y = 0 \).