Final answer:
To solve the system of equations by substitution, solve one equation for a variable, substitute it into the other equation, and solve the resulting quadratic equation. For the given equations, you solve for y first, and then substitute into the second to find x.
Step-by-step explanation:
To solve the system of equations by substitution, you can start by solving one of the equations for one variable and then substituting that expression into the other equation. For the given system:
- x + y = 11
- 4x^2 - 3y^2 = 8
You can solve the first equation for y to get y = 11 - x. Next, you substitute this expression for y into the second equation, resulting in 4x^2 - 3(11 - x)^2 = 8.
From here, you expand and simplify the equation and solve the resulting quadratic equation for x. Once you have x, you plug it back into y = 11 - x to find the corresponding value for y. This method allows you to solve for both x and y and determine the solution to the system of equations.