Solving One-Variable Equations with Systems Assignment

What is x2 + 6x = x2 - 6x as a system? y = x2 + 6xy = x2 - 6x y = -x2 + 6xy = x2 - 6x y = -x2 - 6xy = x2 - 6x

A

2x2 - 3x - 2 = x + 4 The equation is represented by the system shown here. Check all of the solutions to this equation. -1 3 7 (-1, 3) (3, 7)

A & B (-1 , 3)

Both sides of an equation have quadratic expressions. The graph of one quadratic opens upward. The graph of the other opens downward. What are the possible number of intersections for this system? 0 1 2 infinite

A ( 0 ) B (1) C (2)

Which type(s) of equation can have infinite solutions? linear-linear linear-quadratic quadratic-quadratic

A (Linear-Linear) C (Quadratic-Quadratic)

When an equation in one variable is solved using a system of equations, the solution is always the of each intersection.

A (X-Coordinate)

−x2 + x + 6 = 2x + 8 The equation is represented by the system shown here. This system intersects in place(s) Which statement is true? The solution is x = 3. The solutions are x = -2 and x = 3. There are no solutions. There are infinite solutions.

A (Zero) C (There are no solutions)

What is 6x - 8 = 4 written as a system? y = 6x - 8y = -4 y = 6x - 8y = 4 y = -6x + 8y = 4

B

Both sides of an equation have linear expressions. The graph of one line has a positive slope. The graph of the other line has a negative slope. What are the possible number of intersections for this system? 0 1 2 infinite

B (1)

The product property allows an equation in one variable to be written as a system of equations.

B (Substitution)

Which graph shows solving 2x2 - 8x + 5 = -x2 + 4 by graphing a system?

C

Check all of the solutions to the original equation. -9 -6 6 0

D (0)

Describe the graph that would be used to solve the equation -x2 + 4 = x + 2 using a system of equations. How will you use the graph to find the solution(s)?

There is a line and a parabola on the graph. The parabola has a vertex of (0, 4) and opens downward. The line's y-intercept is two, and its slope is one. (Change it up, use quillbot to paraphrase!)