Learn algebra 2 study guides
Introduction:
Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. Algebra 2 study guides 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 guides, we have to use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra 2 study guides may be regarded as an extension of Arithmetic.
Example problems on algebra 2 study guides:
Example 1:
10x + y + 10z = 10 ------------------- (a)
-10x + 2y - 10z = 20 ------------------- (b)
10x - 2y - 2z = 16 ------------------- (c)
Solution:
We have to add (a) and (b)
10x + y + 10z = 10
-10x + 2y - 10z = 20
---------------------
3y = 30 (we have to divide both sides by 20)
(3y) / 3 = 30 / 3
y = 10
we have to add (b) and (c)
-10x + 2y - 10z = 20
10x - 2y - 2z = 16
-----------------------
-12z = 36 ( we have to divide both sides by -12)
(-12z) / -12= 36/ -12
z = -3
Replace y = 10 and z = -3 in (a)
10x + y + 10z = 10
10x + 10 + 10(-3) = 10
10x + 10 - 30 = 10
10x - 20 = 10 ( we have to add 40 on both sides)
10x –20 + 20 = 10 + 20
10x = 30 (divide both sides by 10)
`(10x)/10 = 30/10`
x = 3
Therefore, the answer is x = 3, y = 10 and z = -3
Example 2:
Solve the equation by quadratic formula online 4x2+10x+6=0
Solution:
Here a=4, b=10 and c=6
Discriminant: b2-4ac = 102-4*4*6 = 4
Discriminant (2 is greater than zero.
`x =(-b+-sqrt(b^2-4ac))/(2a)`
`x =(-10+-sqrt(10^2-4*4*6))/(2*4)`
or
`x_1,x_2 = (-10+-2)/(2*4)`
or
x1 = `-8/8` = -1
x2 = `-12/8` = -1.5
or
x1,2= -1 , -1.5
Example 3:
Solve the equation by using the factorization method x2+4x+3=0
Solution:
x2+4x+3=0
x2+3x+x+3=0
(x2+3x)+(x+3)=0
x(x+3)+(x+3)=0
(x+1)(x+3)=0
x+1=0 and x+3=0
x+1-1=0-1 and x+3-3=0-3
x=-1 and x=-3
Therefore, x=-1,-3
Practice problems on algebra 2 study guides:
Problem 1:
12x + 5y + z = 41
15x -2y -6z = 11
2x -5y -2z = -12
Answer: x = 675/293, y = 592/293, z = 953/293
Problem 2:
22x + 52y = 4
52x -22y = 1
Answer: x = 35/797, y = 93/1594
Problem 3:
x² - 2x + 1 = 0
Answer: 1, 1
I like to share this help for 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 guides 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 guides, we have to use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra 2 study guides may be regarded as an extension of Arithmetic.
Example problems on algebra 2 study guides:
Example 1:
10x + y + 10z = 10 ------------------- (a)
-10x + 2y - 10z = 20 ------------------- (b)
10x - 2y - 2z = 16 ------------------- (c)
Solution:
We have to add (a) and (b)
10x + y + 10z = 10
-10x + 2y - 10z = 20
---------------------
3y = 30 (we have to divide both sides by 20)
(3y) / 3 = 30 / 3
y = 10
we have to add (b) and (c)
-10x + 2y - 10z = 20
10x - 2y - 2z = 16
-----------------------
-12z = 36 ( we have to divide both sides by -12)
(-12z) / -12= 36/ -12
z = -3
Replace y = 10 and z = -3 in (a)
10x + y + 10z = 10
10x + 10 + 10(-3) = 10
10x + 10 - 30 = 10
10x - 20 = 10 ( we have to add 40 on both sides)
10x –20 + 20 = 10 + 20
10x = 30 (divide both sides by 10)
`(10x)/10 = 30/10`
x = 3
Therefore, the answer is x = 3, y = 10 and z = -3
Example 2:
Solve the equation by quadratic formula online 4x2+10x+6=0
Solution:
Here a=4, b=10 and c=6
Discriminant: b2-4ac = 102-4*4*6 = 4
Discriminant (2 is greater than zero.
`x =(-b+-sqrt(b^2-4ac))/(2a)`
`x =(-10+-sqrt(10^2-4*4*6))/(2*4)`
or
`x_1,x_2 = (-10+-2)/(2*4)`
or
x1 = `-8/8` = -1
x2 = `-12/8` = -1.5
or
x1,2= -1 , -1.5
Example 3:
Solve the equation by using the factorization method x2+4x+3=0
Solution:
x2+4x+3=0
x2+3x+x+3=0
(x2+3x)+(x+3)=0
x(x+3)+(x+3)=0
(x+1)(x+3)=0
x+1=0 and x+3=0
x+1-1=0-1 and x+3-3=0-3
x=-1 and x=-3
Therefore, x=-1,-3
Practice problems on algebra 2 study guides:
Problem 1:
12x + 5y + z = 41
15x -2y -6z = 11
2x -5y -2z = -12
Answer: x = 675/293, y = 592/293, z = 953/293
Problem 2:
22x + 52y = 4
52x -22y = 1
Answer: x = 35/797, y = 93/1594
Problem 3:
x² - 2x + 1 = 0
Answer: 1, 1
I like to share this help for algebra 2 with you all through my blog.