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 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.

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What is the first step in solving the system: y - 1 = 2x and y = 4x - 1?

Back

The first step is to solve one of the equations for y, which is already done in the second equation: y = 4x - 1.

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What is the solution to the system: y = -2x + 18 and y = 8?

Back

To find the solution, set -2x + 18 = 8, solve for x, and then substitute back to find y. The solution is (5, 8).

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What does it mean if two lines intersect at a point?

Back

If two lines intersect at a point, it means that there is a unique solution to the system of equations represented by those lines.

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What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

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What is the significance of the y-intercept in an equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

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

Back

You can check the solution by substituting the values of x and y back into both original equations to see if they hold true.

Front

What is the solution to the system: y + 8 = 3x and y = 4 - x?

Back

To find the solution, substitute y from the second equation into the first. The solution is (3, 1).