System of Equations Substitution

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 substitution mean in the context of solving equations?

Back

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one of the equations for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the other variable.

Front

What is the first step in solving the system: y = 7x + 9 and 2y + 2x = -18?

Back

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

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What is the solution to the system of equations y = 8x + 1 and y = 6x + 3?

Back

The solution is (1, 9), found by setting the two equations equal to each other and solving for x.

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

Back

A system of equations has no solution if the equations represent parallel lines that never intersect.

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

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Front

In the equation y = x + 5, what is the slope and y-intercept?

Back

The slope is 1 and the y-intercept is 5.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

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