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3 years ago

2y=-x+93×-6y=-15 whats the solution to the system

Mathematics

2 answers:

liq [111]3 years ago

8 0

Answer:

Step-by-step explanation:

2y = -x +9

3x - 6y = -15

The solution is the value of x and y that will make the two equations true in the same time.

3x-6y = -15; divide both sides by 3

x-2y = -5; substitute 2y for -x+9 because the first equation tell us they are equal

x-(-x+9) = -5; open parenthesis

x+x-9 = -5 ; add 9 to both sides and combine like terms

2x = -5 +9; 2x = 4; divide both sides by 2

x= 2

Substitute x for 2

2y = -x+9 ; 2y = -2 +9 ; 2y = 7; y = 7/2 = 3.5

Solution is (2, 3.5)

astraxan [27]3 years ago

3 0

Answer:

(2, 7/2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Coordinates (x, y)
Terms/Coefficients
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

2y = -x + 9

3x - 6y = -15

Step 2: Rewrite Systems

2y = -x + 9

[Division Property of Equality] Divide 2 on both sides: y = -x/2 + 9/2

Step 3: Redefine Systems

y = -x/2 + 9/2

3x - 6y = -15

Step 4: Solve for x

Substitute in y: 3x - 6(-x/2 + 9/2) = -15
Distribute -6: 3x + 3x - 27 = -15
Combine like terms: 6x - 27 = -15
[Addition Property of Equality] Add 27 on both sides: 6x = 12
[Division Property of Equality] Divide 6 on both sides: x = 2

Step 5: Solve for y

Define original equation: 2y = -x + 9
Substitute in x: 2y = -2 + 9
Add: 2y = 7
[Division Property of Equality] Divide 2 on both sides: y = 7/2

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2 years ago

Consider a geometric sequence with a first term of 4 and a fourth term of -2.916.

Orlov [11]

Answer:

a) Find the common ratio of this sequence.

Answer: -0.82

b) Find the sum to infinity of this sequence.

Answer: 2.2

Step-by-step explanation:

nth term in geometric series is given by $4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{0.549} \\r = 0.82$

where

a is the first term

r is the common ratio and

n is the nth term

_________________________________

given

a = 4

4th term = -2.196

let

common ratio of this sequence. be r

$4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{-0.549} \\r = -0.82$

a) Find the common ratio of this sequence.

answer: -0.82

sum of infinity of geometric sequence is given by = a/(1-r)

thus,

sum to infinity of this sequence = 4/(1-(-0.82) = 4/1.82 = 2.2

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3 years ago

ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilatera

Dima020 [189]

Given : - Square ABCD with side 3. E and F as midpoints.
To find : - area of EBFD

Solution : - We have, area of square ABCD = 3 x 3 = 9 units.

Thus, (ar)EBFD = ar ABCD - ar DAE - arDCF

arDAE = 1/2 x base x height

=1/2 x 1.5 x 3 ( AE is 1/2 of AB = 1.5, DA is altitude)
= 2.25

arDFC = 1/2 x base x height
= 1/2 x 1.5 x 3 (FC is 1/2 of BC, DC is altitude)
= 2.25

Thus, (ar) EBFD = arABCD - arDAE - arDCF

= 9 - 2.25 - 2.25

= 4.5 units.

Thus, area of quad EBFD is 4.5 units.

7 0

3 years ago

2y=-x+93×-6y=-15 whats the solution to the system​

2y=-x+93×-6y=-15 whats the solution to the system