Learn algebra 2 study guide
Introduction:
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra 2 study guide cover the four basic operations such as addition, subtraction, multiplication and division. The most important terms of algebra 2 study guides are variables, constant, coefficients, exponents, terms and expressions. In Algebra, 2 study guide, we have to use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra 2 study guide may be regarded as an extension of Arithmetic.
Example problems on algebra 2 study guide:
Example 1:
2x + 2y + z = 4 ------------------- (a)
2x - 2y - z = 4 ------------------- (b)
-2x - y + z = -1 ------------------- (c)
Solution:
We have to add (a) and (b)
2x + 2y + z = 4
2x - 2y - z = 4
---------------------
4x = 8 ( we have to divide both sides by 4)
4x / 4 = 8 /4
x = 2
we have to add (b) and (c)
2x - 2y - z = 4
-2x - y + z = -1
-----------------------
-3y = 3 ( we have to divide both sides by -3)
-3y / -3 = 3/ -3
y = -1
Replace x = 2 and y = -1 in (a)
2(2) + 2(-1) + z = 4
4 – 2 + z = 4
2 + z = 4 ( we have to add -2 on both sides)
2 - 2+ z = 4 – 2
z = 2
Therefore, the answer is x = 2, y = -1 and z = 2.
Example 2:
Use quadratic formula online for solving 2x2 + 8x + 6=0
Solution:
Here a = 2, b = 8 and c = 6
Discriminant: b2-4ac = 82-4*2*6 = 16
Discriminant (16) is greater than zero. The equation has two solutions.
x =(-b±√b2-4ac)/2a
x =(-8±√82-4*2*6)/2*2
or
x1,2 = (-8 ± 4) / 2*2
or
x1 = -4 / 4 = -1
x2 = -12 / 4 = -3
or
x1,2 = -1, -3
Example 3:
Use the factorization method for solving 2x2 + 8x + 6=0
Solution:
2x2 + 8x + 6=0
2x2 + 2x + 6x + 6 = 0
(2x2 + 2x) + (6x + 6) = 0
2x(x + 1) + 6(x + 1) = 0
(x + 1)(2x + 6) = 0
X + 1=0 and 2x + 6 = 0
X + 1 – 1 = 0 - 1 and 2x + 6 – 6 = 0 - 6
x=-1 and x=-3
Therefore, x=-1-3
Practice problems on algebra 2 study guide:
Problem 1:
2 x + 3 y + z = 4
6 x -2 y -6 z = 1
4 x -5 y -2 z = -1
Answer: x = 87/110, y = 37/55, z = 2/5
Problem 2:
2 x + 3 y = 4 6 x -2 y = 1
Answer: x = 1/2, y = 1
Problem 3:
3x² +12x + 9 = 0
Answer: -1, -3
I like to share this help in algebra 2 with you all through my blog.
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra 2 study guide cover the four basic operations such as addition, subtraction, multiplication and division. The most important terms of algebra 2 study guides are variables, constant, coefficients, exponents, terms and expressions. In Algebra, 2 study guide, we have to use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra 2 study guide may be regarded as an extension of Arithmetic.
Example problems on algebra 2 study guide:
Example 1:
2x + 2y + z = 4 ------------------- (a)
2x - 2y - z = 4 ------------------- (b)
-2x - y + z = -1 ------------------- (c)
Solution:
We have to add (a) and (b)
2x + 2y + z = 4
2x - 2y - z = 4
---------------------
4x = 8 ( we have to divide both sides by 4)
4x / 4 = 8 /4
x = 2
we have to add (b) and (c)
2x - 2y - z = 4
-2x - y + z = -1
-----------------------
-3y = 3 ( we have to divide both sides by -3)
-3y / -3 = 3/ -3
y = -1
Replace x = 2 and y = -1 in (a)
2(2) + 2(-1) + z = 4
4 – 2 + z = 4
2 + z = 4 ( we have to add -2 on both sides)
2 - 2+ z = 4 – 2
z = 2
Therefore, the answer is x = 2, y = -1 and z = 2.
Example 2:
Use quadratic formula online for solving 2x2 + 8x + 6=0
Solution:
Here a = 2, b = 8 and c = 6
Discriminant: b2-4ac = 82-4*2*6 = 16
Discriminant (16) is greater than zero. The equation has two solutions.
x =(-b±√b2-4ac)/2a
x =(-8±√82-4*2*6)/2*2
or
x1,2 = (-8 ± 4) / 2*2
or
x1 = -4 / 4 = -1
x2 = -12 / 4 = -3
or
x1,2 = -1, -3
Example 3:
Use the factorization method for solving 2x2 + 8x + 6=0
Solution:
2x2 + 8x + 6=0
2x2 + 2x + 6x + 6 = 0
(2x2 + 2x) + (6x + 6) = 0
2x(x + 1) + 6(x + 1) = 0
(x + 1)(2x + 6) = 0
X + 1=0 and 2x + 6 = 0
X + 1 – 1 = 0 - 1 and 2x + 6 – 6 = 0 - 6
x=-1 and x=-3
Therefore, x=-1-3
Practice problems on algebra 2 study guide:
Problem 1:
2 x + 3 y + z = 4
6 x -2 y -6 z = 1
4 x -5 y -2 z = -1
Answer: x = 87/110, y = 37/55, z = 2/5
Problem 2:
2 x + 3 y = 4 6 x -2 y = 1
Answer: x = 1/2, y = 1
Problem 3:
3x² +12x + 9 = 0
Answer: -1, -3
I like to share this help in algebra 2 with you all through my blog.