Intro to Systems of Equations

What is the solution to a system of equations?

• The solution is the ordered pair (x, y) that satisfies both equations.

• The solution is the sum of the coefficients of the equations.

• The solution is the average of the two equations.

• The solution is the intersection point of the two equations.

What happens to the equation 2x - 6y = 20 when multiplied by -1?

• It becomes -2x + 6y = -20.

• It becomes 2x - 6y = -20.

• It becomes -2x - 6y = 20.

• It becomes 2x + 6y = 20.

How do you graph a system of equations?

• Graph each equation on the same coordinate plane and look for points of intersection.

• Graph each equation separately on different coordinate planes.

• Only graph the first equation and ignore the second.

• Use a table of values for each equation and plot the points.

What is the method of substitution in solving systems of equations?

• The method of substitution involves solving one equation for one variable and substituting that expression into the other equation.

• The method of substitution requires adding both equations together to eliminate one variable.

• The method of substitution involves graphing both equations and finding their intersection point.

• The method of substitution is a technique where you multiply one equation by a constant to match the coefficients.

What is the role of the coefficients in a linear equation?

• Coefficients determine the slope and position of the line on the graph.

• Coefficients represent the y-intercept of the line.

• Coefficients indicate the number of solutions to the equation.

• Coefficients are used to calculate the area under the curve.

What is the slope-intercept form of a linear equation?

• y = mx + b, where m is the slope and b is the y-intercept.

• y = ax^2 + bx + c, a quadratic equation.

• y = mx + c, where m is the slope and c is the y-intercept.

• y = b/x + m, an inverse relationship.

What is a system of equations?

• A set of two or more equations with the same variables.

• A single equation with multiple variables.

• An equation that has no solutions.

• A method to solve quadratic equations.

What are the characteristics of parallel lines in terms of their slopes?

• Parallel lines have different slopes.

• Parallel lines have the same slope.

• Parallel lines intersect at a right angle.

• Parallel lines have slopes that are negative reciprocals.

What does it mean for two lines to coincide?

• They intersect at one point.

• They are parallel and never meet.

• Coinciding lines have the same slopes and the same y-intercepts.

• They are perpendicular to each other.

How do you determine if a system of equations has no solution?

• The lines intersect at one point.

• The lines are parallel (same slope, different y-intercepts).

• The lines coincide (same slope and y-intercept).

• The lines are perpendicular.