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# Algebra - System of Equations and Inequalities

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SOLVE EACH OF THE FOLLOWING PROBLEMS:

#1 Solve the following equation set by substitution:

3x - y = 5

-6x + 2y = 1

#2 Determine the solution set to the following inequality and express using interval notation.

x > 1 and x <= 6

#3 Translate the following verbal expression into an algebraic equation with a single variable-you don't need to solve the equation.

By driving 10 miles per hour slower than Ed, Eunice travels the same distance in 3 hours that Ed travels in 2 hours.

#4 Express the following word problem algebraically and solve the following problem:

Joe must have a take home pay of \$30,400 to live comfortably and pay all his bills. If the government gets 24% of Joe's income, then what must Joe's income be in order for him to live comfortably and pay all this bills.

#5 Simplify the following expression by combining like terms:

5 - 3x(-5x - 2) + 12x^2

#6 Solve: (1/8)(7m - 7) = (2/5)(4m - 4) + 8

#7 Respond True or False to each of the following inequalities?

a. 9 > 9

b. 9 >= 9

#8 Express the answer to the following inequality in interval notation.

(y - 3)/3 > 1/3 - (y - 5)/6

#9 Find the slope and y-intercept for the line given below.

-4x + 2y = 10

#10 Complete the ordered pairs (4, ?) and (?, 5) that satisfy the equation 3x - 6y = 7.

#11 Find the x-intercept and y-intercept of the graph of the following equation.

-3x + y = 12

#12 Find the slope of the line that passes through the points (-9, -9) and (4, -1)

#13 Solve the system by the addition method:

4x + 8y = 6

3x - 8y = 7

#14 Solve the system by the addition method:

(1/6)x + (1/4)y = -2

x - y = -6

#15 Solve the following equation for a:

m = aP - w

#16 Determine which, if any, of the following points satisfy the inequality:

3y - 5x >= 15

Choices: (2, -1); (-3, 0); (0, 5); (-3, -4)

#17 Write the following problem as a system of two equations in two unknowns. Solve the system using the substitution method:

The sum of two numbers is 2, and their difference is 26. Find the numbers.

#18 Solve the following system of equations.

(3/7)x + (5/9)y = 27

(1/9)x + (2/7)y = 7

#19 True or False? The number 5.27 is an integer.

#20 Evaluate the following expression:

(1/2) + (1/3) - (1/6)