Solving Simultaneous Equations with Substitution

This tutorial teaches how to solve simultaneous equations involving a quadratic and a linear equation using the substitution method. It begins with an introduction to the problem, followed by a graphical interpretation of the equations. The method of substitution is explained in detail, leading to the formation of a quadratic equation. The tutorial then demonstrates solving the quadratic equation by factoring and finding the x and y coordinates of the solutions. Finally, the solutions are verified graphically, showing the points of intersection of the parabola and the line.

What does the first equation in a simultaneous equation involving a quadratic and a linear represent?

• A parabola

• A circle

• A straight line

• An ellipse

What is the graphical representation of the solutions to simultaneous equations involving a quadratic and a linear?

• The intersection points of a parabola and a line

• The intersection points of two lines

• The intersection points of a circle and a line

• The intersection points of two parabolas

What is the first step in the substitution method for solving simultaneous equations?

• Eliminate all constants

• Graph the equations

• Make X the subject in both equations

• Make Y the subject in at least one equation

In the substitution method, what do you replace in the second equation?

• Replace X with the expression from the first equation

• Replace the entire equation with a new one

• Replace Y with the expression from the first equation

• Replace the constant term with zero

What is the next step after obtaining an equation without Y in the substitution method?

• Solve for Y

• Gather all terms on one side

• Graph the equation

• Add a constant to both sides

What method can be used to solve the quadratic equation obtained from substitution?

• Factoring or quadratic formula

• Completing the square

• Graphing

• Substitution

What is the null factor law used for in solving quadratic equations?

• To find the sum of roots

• To determine if a product equals zero

• To calculate the vertex of a parabola

• To simplify the equation

What are the x-coordinates of the solutions in the example provided?

• x = 1 and x = -1

• x = -5 and x = 2

• x = 0 and x = 3

• x = 4 and x = -4

Which equation is suggested to use for finding the y-coordinates of the solutions?

• The original equation

• A new equation

• The linear equation

• The quadratic equation

What is the y-coordinate when x equals -5 in the example?

• y = -7

• y = 5

• y = 0

• y = 3