Review: Systems of Linear Equations

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear 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

To solve by substitution, you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the graphical representation of a system of linear equations?

Back

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

Front

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

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

Front

How do you determine the solution of a system of equations graphically?

Back

You plot both equations on a graph and find the point(s) where they intersect.

Front

What is the substitution method for solving the system: x = 2y and 4x + 2y = 15?

Back

Substituting x = 2y into the second equation gives 4(2y) + 2y = 15, which simplifies to 10y = 15, leading to y = 1.5 and x = 3.

Front

How do you solve the system: y = 8x + 2 and y = -x - 7?

Back

Set the equations equal to each other: 8x + 2 = -x - 7. Solving gives x = -1, then substitute back to find y = -6.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

How do you find the value of dimes and nickels in a coin problem?

Back

Set up equations based on the number of coins and their total value, then solve the system of equations.