Checking Solutions for Two Variable Equations

What does the intersection point of two simultaneous equations represent?

• Point of divergence

• Average of the solutions

• Sum of the equations

• Common solution to both equations

Answer explanation

The intersection point of two simultaneous equations represents the common solution to both equations where they meet and have the same values for the variables.

When do simultaneous equations have unique solutions?

• When the equations are independent and the number of equations is less than the number of variables.

• When the equations are dependent and the number of equations is equal to the number of variables.

• When the equations are inconsistent and the number of equations is equal to the number of variables.

• When the equations are independent and the number of equations is equal to the number of variables.

Answer explanation

Simultaneous equations have unique solutions when they are independent and the number of equations is equal to the number of variables.

How can you identify an inconsistent system of simultaneous equations graphically?

• By checking if the graphs are parallel

• By looking at the y-intercepts of the graphs

• By counting the number of variables in the equations

• By plotting the graphs and observing if they intersect at a single point.

Answer explanation

By plotting the graphs and observing if they intersect at a single point.

Find the solution to the system of equations: 4x - 3y = 5 and 2x + 7y = 1

• x = 2, y = -1

• x = -1, y = 2

• x = 5, y = 3

• x = 3, y = 4

Find the solution to the system of equations: 4x - 3y = 5 and 2x + 7y = 1

• x = 2, y = -1

• x = -1, y = 2

• x = 5, y = 3

• x = 3, y = 4

Solve the given pair of linear equations

• x=a + b

  y=-2ab/(a +b)

• x=a -b

  y=2ab/(a-b)

• x=a- b

  y= -2ab/(a-b)

• x=a +b

  y= 2ab/(a +b)

If x=a and y=b is the solution of the equations 2x+ y = 3 and x-y =3, then find the values of a and b

( 1 mark )

Evaluate responses using AI:

OFF

What does it mean when two simultaneous equations graph as parallel lines?

• The equations have the same slope but different y-intercepts.

• The equations have different slopes and different y-intercepts.

• The equations have the same slope and the same y-intercept.

• The equations intersect at multiple points.

Answer explanation

When two simultaneous equations graph as parallel lines, it means they have the same slope but different y-intercepts.

Explain the substitution method for solving simultaneous equations.

• The substitution method involves graphing the equations to determine the solution

• The substitution method involves solving one equation for one variable, substituting that expression into the other equation, solving for the remaining variable, and then finding the other variable by substituting back into one of the original equations.

• The substitution method involves multiplying both equations to find the common solution

• The substitution method involves adding both equations together to eliminate one variable

Answer explanation

The substitution method involves solving one equation for one variable, substituting that expression into the other equation, solving for the remaining variable, and then finding the other variable by substituting back into one of the original equations.

Describe the elimination method for solving simultaneous equations.

• The graphical method involves plotting the equations on a graph and finding the intersection point.

• The matrix method involves representing the equations in matrix form and using matrix operations to solve.

• The substitution method involves multiplying one or both equations by a constant to make the coefficients of one variable the same.

• The elimination method for solving simultaneous equations is a technique where you add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.

Answer explanation

The elimination method involves adding or subtracting the equations to eliminate one variable, simplifying the process of solving for the remaining variable.