Solving Systems of Equations (All Methods)

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 for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What is the solution to the system of equations: y = -x + 5 and y = 2x - 7?

Back

(4, 1)

Front

Solve the system of equations: y = 4x + 1 and 3x + 2y = 13.

Back

(1, 5)

Front

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

Back

(-1, 1)

Front

Solve for x and y: 5x + 3y = 7 and y = 4.

Back

(-1, 4)