26 Algebra Problems

Please refer to the attachment for the solutions.

Build up the following fraction so that it is equivalent to the fraction on the left hand side of the equation.

Solution:

Perform the indicated operations without using a calculator.

 -10 - 18 =
 -1 + (-20) =

Solution: -10 - 18 = -28
-1 + (-20) = -21

Determine if x = 2 is a solution to the following equation

Solution: Putting x =2 in the above equation we get
Therefore, x = 2 is a solution to the given equation

Simplify the following expressions by combining like terms

Solution:

Solve the following equation for x. Show your work and check your answer.

Solution: 12x = -3.75+2.1 = -1.65
Or, x = -1.65/12 = -0.1375

Solve the following equation for a. Show your work and check your answer.

Solution:
Or,
Or,
Or, a = 6

Find two consecutive even integers whose sum is 50
Solution: Let one integer be x. Then the other is (x+2)
x+x+2=50
Or, 2x = 50-2=48
Or, x = 48/2=24
Therefore, the integers are 24 and 24+2=26.

Solve the following equation for a. Show your work and check your answer.

Solution:

Solve the following equation for x. Show your work and check your answer.

Solution: 2x + 2 = 5
Or, 2x = 5-2=3
Or, x = 3/2 = 1.5

Solve the following equation for v. Show your work and check your answer.

Solution:
Or,
Or,
Or,
Or,

Graph the line that goes through the point (-1, 2) with slope -1
Solution: (y-2) = -1(x+1)
Or, y = -x +1

Graph the line that goes through the point (0, 3) with slope -2
Solution: (y-3) = -x
Or, y = -x+3

Find the slope and y-intercept for the line below
.

Solution: y = -3+ 2x
Slope = 2
y-intercept = -3

Find the slope and y-intercept for the line below
.

Solution: y = 3x+ 2
Slope = 3
y-intercept = 2

Determine if the following two lines are parallel, perpendicular or neither

Solution: Parallel

Determine if the following two lines are parallel, perpendicular or neither

Solution: Perpendicular

Find the equation of the line that is parallel to the line given and passes through the point given

Solution: Slope = -1
The equation of the line that is parallel to the line is given as

Find the equation of the line that is perpendicular to the line given and passes through the point given

Solution: Slope = 2
The equation of the line that is parallel to the line is given as

Write a formula that expresses the relationship described by the following statement

Y varies directly as R

Solution: Y = k R
where k is the constant of proportionality.
Solve the following system of equations by substitution. Determine whether the equations are independent, dependent or inconsistent.

Solution: Putting y = x+8 from the second equation in the first equation, we get
x + 8 = 4x - 1
Or, 9 = 4x - x = 3x
Or, x = 9/3 = 3
Putting x = 3 in the second equation, we get y = 3+8 = 11

Solve the following system of equations by substitution. Determine whether the equations are independent, dependent or inconsistent.

Solution: From the first equation,
2x = -4y
Or, x = -4y/2 = -2y
Putting x = -2y in the second equation, we get
-12y+8y = 5
Or, -4y = 5
Or, y = -5/4
Therefore, x = -2 -5/4 = 5/2

Solve the following system of equations by substitution. Determine whether the equations are independent, dependent or inconsistent.

Solution: From the second equation, y = 3x/7
Putting y = 3x/7 in the first equation, we get
x = -9x/7 +2
Or, 16x/7 = 2
Or, x = 7/8
Therefore, y = 3/8

Solve the following system of equations by addition. Determine whether the equations are independent, dependent or inconsistent.

Solution: Adding the two equations together, we get
x - y + x + y = 1+1
Or, 2x = 2
Or, x = 2/2=1
Putting x = 1 in the first equation, we get
1-y = 1
Or, y = 0

Solve the following system of equations by addition. Determine whether the equations are independent, dependent or inconsistent.

Solution:
[1]

Subtracting [2] from [1]:

-23y = 69

Putting y = -3 in [1]:

Solve the following system of equations by addition. Determine whether the equations are independent, dependent or inconsistent.

Solution: [3]
Adding [2] and [3]:

The length of a rectangular photo is 2 inches greater than the width. The perimeter is 20 inches. Find the length and width.

Solution:

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