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)
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