Solve the system of equations using substitution. x=1 y=6 -x+y=5 y=(x-3)^2+2

1 answer

Let's solve the system of equations given:

  1. \( x = 1 \)
  2. \( y = 6 \)
  3. \( -x + y = 5 \)
  4. \( y = (x - 3)^2 + 2 \)

From the first two equations, we have \( x = 1 \) and \( y = 6 \).

Let's check if these values satisfy the other two equations.

Checking the third equation: \[ -x + y = 5 \] Substituting \( x = 1 \) and \( y = 6 \): \[ -1 + 6 = 5 \] This equation is satisfied.

Checking the fourth equation: \[ y = (x - 3)^2 + 2 \] Substituting \( x = 1 \): \[ y = (1 - 3)^2 + 2 \] Calculating the right side: \[ y = (-2)^2 + 2 = 4 + 2 = 6 \] This equation is also satisfied.

Since all equations are satisfied by \( x = 1 \) and \( y = 6 \), the solution to the system of equations is: \[ \boxed{(1, 6)} \]