Solving Systems of Equations Using Substitution Practice

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean to solve a system of equations using substitution?

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Solving a system of equations using substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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How do you represent the total number of students in two teams with variables?

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If the field hockey team has 12 more students than the soccer team, how can this be expressed?

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The first step is to substitute the expression for y from the second equation into the first equation.

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What does it mean if two equations in a system have no solution?

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If two equations have no solution, it means they are parallel lines that never intersect.

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What does it mean if two equations in a system have infinitely many solutions?

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If two equations have infinitely many solutions, it means they represent the same line, and every point on that line is a solution.

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What is the graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection points of the lines represented by the equations.

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How can you check your solution to a system of equations?

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You can check your solution by substituting the values back into the original equations to see if they hold true.