Simultaneous Equations Graphing Vocab

How can simultaneous equations be solved using the graphing method?

• Solve one equation at a time

• Use substitution method

• Graph each equation and find the point of intersection.

• Guess and check method

Answer explanation

To solve simultaneous equations using the graphing method, graph each equation on the same coordinate plane and find the point where they intersect.

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.

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.

When do simultaneous equations have no solution?

• When the lines are parallel

• When the lines are perpendicular

• When the lines are vertical

• When the lines intersect at a single point

Answer explanation

Simultaneous equations have no solution when the lines are parallel, as they will never intersect.

How can you graph two parallel lines on the coordinate plane?

• Graph two lines with equations y = mx + b1 and y = mx + b2, where m is the slope and b1, b2 are different y-intercepts.

• Graph two lines with equations y = mx + b1 and y = mx + b2, where m is the slope and b1, b2 are the same y-intercepts.

• Use different slopes for the two lines but have the same y-intercept.

• Graph two lines with equations y = mx + b1 and y = mx + b1, where m is the slope and b1 is the y-intercept.

Answer explanation

Graph two lines with equations y = mx + b1 and y = mx + b2, where m is the slope and b1, b2 are different y-intercepts.

What is the significance of the slope of the lines in simultaneous equations?

• The slope of the lines in simultaneous equations has no impact on the solution

• The slope of the lines in simultaneous equations is always equal

• The slope of the lines in simultaneous equations determines the relationship between the lines - parallel, intersecting at one point, or overlapping.

• The slope of the lines in simultaneous equations determines the y-intercept

Answer explanation

The slope of the lines in simultaneous equations determines the relationship between the lines - parallel, intersecting at one point, or overlapping.