Systems of Equations and Their Solutions

The point where two lines cross on a graph.

A pair of numbers that show the location of a point on a graph.

A straight line drawn on a graph.

The equation that represents the relationship between the variables of a line.

A system of equations has infinitely many solutions if the two equations represent the same line. This means that the equations are equivalent, or one is a multiple of the other.

To determine if an equation represents the same line as the given graph, check if the equation is equivalent to the slope-intercept form of the line in the graph. This means you need to solve the equation for y.

A coordinate pair represents a point on a graph. The first number in the pair represents the x-coordinate (horizontal position) and the second number represents the y-coordinate (vertical position).

The graph shows a line passing through the points (0, 3) and (2, 0). To find the coordinate pair for the point where the line crosses the y-axis, look for the y-coordinate when x is 0.

The coordinate pair where the line crosses the y-axis is the point where the x-coordinate is 0. In this case, the y-coordinate is 3. Therefore, the correct coordinate pair is (0, 3).

A set of two or more equations that share the same variables and need to be solved simultaneously.

The point where two lines intersect, representing a solution that satisfies both equations in the system.

The initial value of y when x is zero, represented as the point where the line intercepts the y-axis on a graph.

The equations have the same slope, meaning they are parallel and will never intersect. This means there is no point where the x and y values satisfy both equations, resulting in no solution.

The y-intercept is where the line crosses the y-axis. If the equations have opposite y-intercepts, it means they will intersect at some point, leading to one solution.

A system of equations has a solution when the lines represented by the equations intersect at a single point. This point represents the coordinate values that satisfy both equations.

To solve a system of equations, you need to find the values of the variables that satisfy both equations simultaneously. This can be done using methods like substitution or elimination.

In a system of equations, each equation represents a line. The solution to the system is the point where these lines intersect. This point represents the coordinate values that satisfy both equations.

The solution to a system of equations is a pair of values - one for each unknown variable - that make both equations true.

Different systems of equations can have different numbers of solutions. A system can have no solutions, one solution, or infinitely many solutions.