Solving Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

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

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation(s).

Front

What is the first step in solving a system of equations using substitution?

Back

Identify one equation to solve for one variable in terms of the other variable.

Front

If you have the equations y = 2x + 3 and 4x - y = 5, how would you solve it using substitution?

Back

First, solve the first equation for y: y = 2x + 3. Then substitute this expression for y in the second equation: 4x - (2x + 3) = 5.

Front

What is the solution to the system of equations: x + y = 5 and x - y = 1?

Back

The solution is (3, 2).

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What does it mean if a system of equations has no solution?

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It means that the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

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It means that the equations represent the same line, and every point on that line is a solution.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations.

Front

What is the substitution method used for?

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The substitution method is used to find the values of variables that satisfy all equations in a system.