linear Equations in two Variables

What does it mean for two lines to be coincident?

• They intersect at a single point.

• They are parallel and never meet.

• They lie on top of each other, meaning they have the same slope and y-intercept.

• They have different slopes and will eventually cross.

What is a linear equation in two variables?

• An equation that can be expressed in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

• An equation that represents a straight line on a graph.

• An equation that involves only one variable.

• An equation that can be expressed in the form x^2 + y^2 = c.

How do you find the x-intercept of a linear equation?

• Set y = 0 in the equation and solve for x.

• Set x = 0 in the equation and solve for y.

• Add the coefficients of x and y together.

• Multiply the equation by -1.

What is the graphical representation of a system of equations with no solution?

• Two intersecting lines

• Two parallel lines that never intersect

• A single line

• Two lines that meet at a point

What is the elimination method for solving systems of equations?

• The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

• The elimination method requires multiplying both equations by a constant before adding them.

• The elimination method is used to graph equations on a coordinate plane.

• The elimination method involves substituting one variable into the other equation.

What does it mean for a pair of linear equations to be consistent?

• A pair of linear equations is consistent if there is at least one solution, meaning the lines represented by the equations intersect at one point or are coincident.

• A pair of linear equations is consistent if they have no solutions, meaning the lines are parallel.

• A pair of linear equations is consistent if they are identical, meaning they represent the same line.

• A pair of linear equations is consistent if they intersect at multiple points, meaning they are dependent.

What is the relationship between the coefficients of two equations for them to be parallel?

• The ratio of the coefficients of x and y must be the same, and the constant terms must also be the same.

• The ratio of the coefficients of x and y must be the same, but the constant terms must differ.

• The coefficients of x and y must be equal for both equations.

• The constant terms must be equal for the equations to be parallel.

How can you represent a word problem as a system of equations?

• Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

• Write down the problem statement without any changes.

• Use only one variable to simplify the problem.

• Ignore the relationships and focus on the final answer.

How can you determine if a system of equations is inconsistent?

• A system of equations is inconsistent if the equations represent parallel lines, which have no points of intersection.

• A system of equations is inconsistent if it has at least one solution.

• A system of equations is inconsistent if the equations represent the same line.

• A system of equations is inconsistent if it has infinitely many solutions.

What is the y-intercept of a linear equation?

• The point where the line crosses the x-axis.

• The point where the line crosses the y-axis, found by setting x = 0 in the equation.

• The slope of the line when x = 0.

• The value of y when x is at its maximum.