EE7 (Number of Solutions of Linear Equations)

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean for a linear equation to have one solution?

Back

A linear equation has one solution when the graph of the equation intersects the x-axis at exactly one point.

Front

What does it mean for a linear equation to have infinitely many solutions?

Back

A linear equation has infinitely many solutions when the two sides of the equation are equivalent for all values of x, resulting in the same line on a graph.

Front

What does it mean for a linear equation to have no solution?

Back

A linear equation has no solution when the lines represented by the equations are parallel and never intersect.

Front

How do you determine the number of solutions for a system of linear equations?

Back

You can determine the number of solutions by graphing the equations and observing their intersection points: one solution (intersecting), infinitely many solutions (same line), or no solution (parallel lines).

Front

What is the sales tax rate in Langston's guitar purchase problem?

Back

The sales tax rate is 7%.

Front

If Langston has $62 and needs $200 plus sales tax, how much more money does he need?

Back

Langston needs $200 + (7% of $200) = $200 + $14 = $214. He has $62, so he needs $214 - $62 = $152 more.

Front

How much does Langston save from his weekly earnings?

Back

Langston saves half of his weekly earnings of $22, which is $11.

Front

How many weeks will it take Langston to save enough for the guitar?

Back

Langston needs $152 more and saves $11 per week. It will take 152 / 11 = approximately 13.82 weeks, which rounds up to 14 weeks.

Front

What is the solution for x in the equation 5(x−4)=2+3x?

Back

The solution for x is 11.