Solving Problems Using Equations and Inequalities

Equations that have the exact same solutions.

• equivalent equations

• expressions

• constraint

• ratios

Answer explanation

Equations that have the exact same solutions are equivalent equations.

A coordinate pair that makes both equations in the system true.

• solution to a system of equations

• expression

• constant of proportionality

• rate of change

Answer explanation

A coordinate pair that makes both equations in the system true is called a solution to a system of equations.

On the graph shown of the equations in a system, the solution is the point where the graphs intersect. In this system, the solution is (2,3).

A method of solving a system of two equations in two variables where you add or subtract a multiple of one equation to another in order to get an equation with only one of the variables.

Answer explanation

Elimination is a method of solving a system of two equations in two variables where you add or subtract a multiple of one equation to another in order to get an equation with only one of the variables (thus eliminating the other variable).

All pairs of values that make the inequalities in a system true are solutions to the system. This can be represented by the points in the region where the graphs overlap.

• solutions to a system of inequalities

• system of inequalities

• system of equations

• variables

Answer explanation

Solutions to a system of inequalities are all pairs of values that make the inequalities in a system true are solutions to the system. The solutions to a system of inequalities can be represented by the points in the region where the graphs of the two inequalities overlap.

Solve the equation shown.

Show the work you do in finding your final answer on the paper provided.

Mathematical Equivalence

ON

Answer explanation

Two or more equations that represent the constraints in the same situation form this.

Answer explanation

Two or more equations that represent the constraints in the same situation form a system of equations.

Two systems are this if they share the exact same solution set.

• equivalent systems

• negative

• parallel

• perpendicular

Answer explanation

Two systems are equivalent if they share the exact same solution set.

Two or more inequalities that represent the constraints in the same situation.

• system of inequalities

• system of equations

• equations

• expressions

Answer explanation

Two or more inequalities that represent the constraints in the same situation form a system of inequalities.

Select all of the correct answers

*Hint: we worked on these types of problems over the past two weeks!

• Solve a system of equations by graphing

• Solve a system of equations using elimination

• Solve a system of equations using any method

• Solve a system of equations using slope and y-intercept

• Solve a system of equations using substitution

Mr. Cain just had his condo appraised to find out its value. According to the appraiser, the condo is currently worth $641,655. That is 50% higher than the condo was worth when he bought it several years ago. What was the value of the condo then?

• $641,655

• $427,770

• $213,885

• $320,827