Solving Systems by 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 point(s) where the equations intersect.

Front

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

Back

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the first step in solving the system of equations y = 2x + 1 and y = 4x - 1 by substitution?

Back

The first step is to set the two equations equal to each other since they both equal y: 2x + 1 = 4x - 1.

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3).

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What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have no points of intersection, indicating that the system has no solution.

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What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

The solution is (3, 1).

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

Back

You can check your solution by substituting the values back into the original equations to see if both equations are satisfied.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.