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3 years ago

How to solve system by substitution X+y=10 X-y=2

Mathematics

1 answer:

PtichkaEL [24]3 years ago

8 0

Answer:

x = 6 , y = 4

Step-by-step explanation:

Solve the following system:

{x + y = 10

x - y = 2

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{x + y = 10

x - y = 2

Hint: | Solve for y.

Subtract x from both sides:

{y = 10 - x

x - y = 2

Hint: | Perform a substitution.

Substitute y = 10 - x into the second equation:

{y = 10 - x

2 x - 10 = 2

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{y = 10 - x

2 x - 10 = 2

Hint: | Isolate terms with x to the left hand side.

Add 10 to both sides:

{y = 10 - x

2 x = 12

Hint: | Solve for x.

Divide both sides by 2:

{y = 10 - x

x = 6

Hint: | Perform a back substitution.

Substitute x = 6 into the first equation:

{y = 4

x = 6

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 6 , y = 4

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Could someone please help me with this? I would mark you as Brainliest:)

Hunter-Best [27]

Answer:

a) The table of values represents the ordered pairs formed by the elements of the sequence ( $a_{i}$ ) (range) and their respective indexes ( $i$ ) (domain):

$i$ $a_{i}$

1 6

2 11

3 16

4 21

5 26

b) The algebraic expression for the general term of the sequence is $a(i) = 6 + 5\cdot (i - 1)$ .

c) The 25th term in the sequence is 126.

Step-by-step explanation:

a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...

The table of values represents the ordered pairs formed by the elements of the sequence ( $a_{i}$ ) (range) and their respective indexes ( $i$ ) (domain):

$i$ $a_{i}$

1 6

2 11

3 16

4 21

5 26

b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:

$a(i) = a_{1} + r\cdot (i - 1)$ (1)

Where:

$a_{1}$ - First element of the sequence.

$r$ - Arithmetic difference.

$i$ - Index.

If we know that $a_{1} = 6$ and $r = 5$ , then the algebraic expression for the general term of the sequence is:

$a(i) = 6 + 5\cdot (i - 1)$

c) If we know that $a(i) = 6 + 5\cdot (i - 1)$ and $i = 25$ , then the 25th term in the sequence is:

$a(25) = 6 + 5\cdot (25 - 1)$

$a(25) = 126$

The 25th term in the sequence is 126.

7 0

2 years ago

Line 1 passes through the points -2,7 and 3,3. Line 2 passes through the points 5,1 and 9,1. Find the slope of each line. Which

RSB [31]

Answer:

The slope of the given line 1 is -4/5.

The slope of the given line 2 is 0.

The line 2 has a greater slope then line 1.

Step-by-step explanation:

The slope of a line with points (x1,y1) and (x2,y2) is given as:

$m = \frac{y_2- y_1}{x_2-x_1}$

Now, Here the, points of the line 1 are A (-2,7) and B (3,3)

So, here, the slope of line AB is $m = \frac{3 -7}{3-(-2)} = \frac{-4}{3 +2} = \frac{-4}{5}$

Hence, the slope of the given line 1 is -4/5.

Now, Here the, points of the line 2 are P (5,1) and Q (9,1)

So, here, the slope of line PQ is $m = \frac{1-1}{9-5} = \frac{0}{4} = 0$

Hence, the slope of the given line 2 is 0.

Now, as we can see 0 > ( -4 / 5)

So, the line 2 has a greater slope then line 1.

5 0

2 years ago

the length of a flag is 0.3 foot less than twice its width. if the perimeter is 14.4 feet longer than the width, find the dimens

forsale [732]

$x-\ length\\
y-\ width\\\\
x+0.3=2y\ \ \ \ \ | subtract\ 0.3\\x=2y-0.3\\
perimeter=2x+2y\\ 2x+2y-14.4=y\\\\
2*(2y-0.3)+2y-14.4=y\\
4y-0.6+2y-14.4=y\\
6y-15=y\ \ \ | add\ 15\\
6y=15+y\ \ | subtract\ y\\
5y=15\ \ \ | divide\ by\ 5\\
y=3\\
x=2y-0.3=2*3-0.3=6-0.3=5.7\\\\
Dimensions:\ length=5.7\ feet\, width=3\ feet.$

4 0

3 years ago

What is 9 times 2/6 in multiply fractions and whole numbers

lawyer [7]

- - Let's solve:

$\frac{9}{1} * \frac{2}{6}$

$= \frac{9}{1} * \frac{1}{3}$

$= \frac{9*1}{1*3}$

$= \frac{9}{3}$

$=3$

8 0

3 years ago

Read 2 more answers

Dustin has only nickels and quarters in his piggy bank. He was 49 total for combined value of $8.85. How many of each type of co

Troyanec [42]

Let's use the variables N and Q for the number of nickels and the number of quarters.

We know there are 49 total coins, so we can write the following equation:

N + Q = 49

We can solve this equation for one variable which will help in the next step. Let's solve for N:

N = 49 - Q

Next, we know that nickels are worth $0.05 and quarters are worth $0.25. We can use these values along with the total value of $8.85 to create another equation.

0.05N + 0.25Q = 8.85

Now we can use substitution to solve our system out equations. We solved the first equation for N, so we can plug 49 - Q in for N.

0.05(49-Q) + 0.25Q = 8.85

Distribute and combine like terms.

2.45 - 0.05Q + 0.25Q = 8.85

2.45 + 0.2Q = 8.85

0.2Q = 6.4

Q = 32

Plug 32 in for Q in N + Q = 49 to find the number of nickels.

N + 32 = 49

N = 17

Dustin has 32 quarters and 17 nickels.

4 0

3 years ago