Math Study Set For Unit 5

John is twice as old as Mary. The sum of their ages is 52. How old is Mary? If J = John's age and M = Mary's age, which system of equations could be used to solve the problem?

J = 2M and J + M = 52

linear inequality

an open sentence of the form Ax + By + C < 0 or Ax + By + C > 0

consistent equations

equations having a common solution in a system

equivalent equations

equations having all common solutions

inconsistent equations

equations having no common solutions in a system

substitute

replace a quantity with its equal

x-determinant

the determinant found when column 1 consists of the constants and column 2 consists of the y-coefficients of a linear system

y-determinant

the determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system

system determinant

the determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system

$1,500 is invested in two different accounts paying 4% and 5% interest. If a total of $67 interest is earned after one year, then how much money was invested at 4%?

$800

The lines whose equations are 2x + y = 3z and x + y = 6z intersect at which point?

(-3z, 9z)

If a boat that travels 23 miles per hour in still water is traveling with a current that has a rate of 2 miles per hour, how far will the boat travel in 3 hours?

75 miles

Given the system of equations, what is the value of the system determinant? 2x + y = 8 x - y = 10

-3

Solve the following system of equations by the substitution method. 5x = y + 6 2x - 3y = 4 What is the value of the y-coordinate?

-8/13

Which of the following equations is equivalent to y = 2/3x + 1/4?

12y = 8x + 3