Solve each system. Then check each solution and Identify any extraneous solutions. Show your work for partial credit. 1. y=(2x-5)^(1)/(2) 2x+y=7 2. 3x+2y=9 3. y=-4x^2+3x+8 y=2x^2+3x-16

1. To solve the system of equations, we can substitute the expression for y from the first equation into the second equation: Substituting the expression for y into the second equation, we get: To solve this equation, we can square both sides to eliminate the square root: Expanding and simplifying, we get: This equation is quite complex to solve directly. We can try another approach by substituting the expression for y into the second equation and solving for x: Let , then the equation becomes: Solving for x, we get: Substituting this back into the expression for y, we get: Simplifying, we get: Now we have two expressions for y in terms of u. Equating them, we get: Squaring both sides, we get: Expanding and simplifying, we get: Solving for u, we get: Substituting this back into the expression for x, we get: So the solution to the system of equations is and .2. To solve the system of equations, we can use the substitution method. Let's solve for x in the first equation: Now substitute this expression for x into the second equation: Simplifying this equation, we get: $y = -\frac{4}{9}(81 - 36y + 4y^2) - 2y + 17