Final answer:
To solve the system of equations using substitution method, first solve one equation for one variable in terms of the other. Then, substitute this expression into the other equation and solve for the variable. Finally, substitute the found values into the expression for the other variable to determine the solutions. the solutions to the system of equations are (x, y) = (2.5, 0.5) and (2, 1).
Step-by-step explanation:
To solve the system of equations using substitution method:
Step 1: Use the first equation to solve for one variable in terms of the other.
x + y = 3, so x = 3 - y.
Step 2: Substitute the expression for the variable found in step 1 into the second equation.
y = 4(3 - y)² - 2
Step 3: Simplify and solve the quadratic equation to find the value of y.
16y² - 24y + 10 = 0
Solving this quadratic equation gives y = 0.5 or y = 1.
Step 4: Substitute the values of y into the expression for x found in step 1.
If y = 0.5, then x = 3 - 0.5 = 2.5.
If y = 1, then x = 3 - 1 = 2.
Therefore, the solutions to the system of equations are (x, y) = (2.5, 0.5) and (2, 1).