Solving One-Variable Equations with Systems Answers

Which graph can be used to find the solution(s) to x2 – 4x + 4 = 2x + 1 + x2?

Tiffany is solving an equation where both sides are quadratic expressions. She sets each quadratic equation equal to y and graphs the resulting system. If the graph of one quadratic opens upward and the other opens downward, what is the greatest possible number of intersections for these graphs?

What are the two solutions of 2x2 = –x2 – 5x – 1?

Carlos graphs the equations y = 0.5x2 + 3 and y = –4x2 + 24x – 35 and generates the graph below. Which conclusion is supported by the graph?

Which graph can be used to find the solution(s) to x2 – 1 = 3?

Vivek graphs the equations and to solve the equation . His graph is shown below. What are the solutions of ?

Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Fran graphs the equations and . Her graph is shown below. Which value is a solution of ?

Which graph can be used to find the solution(s) to x2 – 1 = x + 1?

Heather is solving an equation by graphing the expressions on either side of the equal signs. If the graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?

What is the solution of 3x + 5 = 2x – 7?

Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below.What are the solutions of –x2 + 4x = x – 4?

Michael graphs the equations and y = x + 1 to solve the equation . His graph is shown below. What are the solution(s) of ?

Which system of equations can be graphed to find the solution(s) to ?

Which system of equations can be graphed to find the solution(s) to x2 = 2x + 3?