Solve the system below using SUBSTITUTION. Show step-by-step work to earn credit. Use the Formula Editor x−−√ to type math or use the Image icon to upload a photo of your work.

x+y=4
y=7x+4

1 answer

To solve the system of equations using substitution, we start with the given equations:

  1. \( x + y = 4 \)
  2. \( y = 7x + 4 \)

Step 1: Solve for one variable

We will use the first equation to express \( y \) in terms of \( x \).

From the equation: \[ y = 4 - x \]

Step 2: Substitute into the second equation

Now we will substitute \( y \) from the first equation into the second equation.

The second equation is: \[ y = 7x + 4 \]

Substituting \( y \): \[ 4 - x = 7x + 4 \]

Step 3: Solve for \( x \)

Now we will solve the equation for \( x \).

First, we will simplify the equation: \[ 4 - x = 7x + 4 \]

Subtracting \( 4 \) from both sides: \[ -x = 7x \]

Now, add \( x \) to both sides: \[ 0 = 8x \]

Dividing both sides by \( 8 \): \[ x = 0 \]

Step 4: Substitute \( x \) back to find \( y \)

Now we can substitute \( x = 0 \) back into the first equation to find \( y \): \[ y = 4 - x \] \[ y = 4 - 0 \] \[ y = 4 \]

Conclusion

The solution to the system of equations is: \[ (x, y) = (0, 4) \]

Summary of the solution:

  1. From \( x + y = 4 \), we found \( y = 4 - x \).
  2. Substituted \( y = 4 - x \) into \( y = 7x + 4 \), leading to the equation \( 4 - x = 7x + 4 \).
  3. Solved for \( x \) and found \( x = 0 \).
  4. Substituted \( x = 0 \) back to find \( y = 4 \).
  5. Therefore, the solution is \( (0, 4) \).