#Homework Help Please

Solve the system by substitution. x= 2y + 7 3x – 2y = 3 The solution is?

seropon [69]

Hi there! Your answer is x = -2, y = -9/2

In coordinate point, we can write (-2,-9/2)

Please see the explanation below for a clear understand about the problem.

Any questions about the answer, feel free to ask in comment! :)

Step-by-step explanation:

Goal

Solve the system of equations by substitution method.

Given

System of Equations

$\begin{cases} x=2y+7 \Longrightarrow (1)\\ 3x-2y=3 \Longrightarrow (2) \end{cases}$

Step 1

Since our x-term is the subject in the first equation, we can simply substitute x = 2y+7 in the second equation.

Substitute x = 2y+7 in the second equation.

$3x-2y=3\\3(2y+7)-2y=3$

We do this so we can solve for the y-term without any problems. (We need to get rid of a variable if there are more than one variable.)

Then we distribute/expand 3 in the expression.

$6y+21-2y=3\\4y+21=3$

Step 2

Solve the equation for y-term

To solve the equation, we have to isolate the term that we want. For this scenario, we want to know the value of y-term. Therefore, we isolate y-term.

$4y=3-21\\4y=-18\\y=-\frac{18}{4} \\y=-\frac{9}{2}$

Finally! we know the value of y which is -9/2. But we are not done yet!

Step 3

Substitute the y-value in any given equations.

After we solve the equation, we have to substitute the value in any given equations. No need to substitute the value in both equations! Choose an equation to substitute the value in.

For this, I will be choosing an equation with less coefficients which is the first equation.

$x=2y+7$

Substitute y = -9/2 in the equation.

$x=2(-\frac{9}{2})+7\\x=-9+7\\x=-2$

We should get x = -2 as the answer. This is our last step for finding an answer. The next few steps are going to be how to check the answer for system of equations. Note that next few steps are optional. If you are not certain that the answer is wrong or right, it is highly advised to check the answer before jumping to a conclusion!

Optional Steps - Answer Check

To check the answer, we can simply substitute both x-value and y-value in any given equations. You can either choose only a single equation to substitute in ONLY if you are certain/sure that the answer is likely correct. Substituting in both equations are recommended for beginners.

Step 3

Substitute x = -2 and y = -9/2 in the system of equations.

Step 3.1

Substitute in x = 2y+7

$x=2y+7$

From x = -2 and y = -9/2

$-2=2(-\frac{9}{2} )+7$

Cancel 2 out.

$-2=-9+7\\-2=-2$

As you can see, both sides are equal. That means the equation is true for x = -2 and y = -9/2.

Step 3.2

Substitute in 3x-2y = 3

$3x-2y=3$

Substitute x = -2 and y = -9/2 in the equation.

$3(-2)-2(-\frac{9}{2})=3\\-6+\frac{18}{2}=3\\-6+9=3\\3=3$

Since both equations are true for x = -2 and y = -9/4. We can conclude that:

$\huge\sf{x = -2 \ and \ y = -\frac{9}{2} \ are \ the \ solutions \ to \ the \ system \ of \ equations.}$

Hence, the answer is x = -2 and y = -9/2.

5 0

3 years ago

Given the endpoints of a segment, find the length of each segment. A (-3, 7) and B (-5, 2)

Illusion [34]

Step-by-step explanation:

Using the distance formula

√(x1-x2)²+(y1-y2)²

√(-3+5)²+(7-2)²

√(2)²+(5)²

√4+25

√29 units

<h2>MARK ME AS BRAINLIST </h2>

6 0

2 years ago

You purchase a total of 45 shares of stocks from 3 different companies. You purchase twice as many shares of company c stock as

bearhunter [10]

A)The total cost would be: x=15a+12b+18c where x is the total cost and a,b,and c are the amount of stocks you bought from their respective companies.

B) Since you bought 10 A stocks, you must have bought 20 C stocks. That adds up to 30 bought, leaving 15 for B.

x=(15)(10)+(12)(15)+(18)(20)
x=150+180+360=$690 spent

C) A's stock is now 15(1.25) which is 18.75. C's stock is now 18(.90) which is 16.2
new equation is 18.75a+12b+16.2c=x

D) Substitute the number of stocks we bought from each in again:
187.5+180+324=$691.5

The cost went up slightly, so divide 690/691.5 then multiply that number by one hundred. You get that you spent in B 99.8% the amount you spent in C. So 100-99.8= an increase of .2% 

8 0

4 years ago

A flagpole broke in a storm. 7 meters are still sticking straight out of the ground, where it snapped, but the remaining piece h

serious [3.7K]

32 meters tall.
It would form a right triangle, in which the shorter leg is 7m and the longer leg is 24m. You're looking for the last side, the hypotenuse. So use the Pythagorean theorem. a^2 + b^2 = c^2 , in which a and b are the legs and c is the hypotenuse.
Therefore, you get 7^2 + 24^2 = c^2.
Which is, 49 + 576 = c^2
Add, 625 = c^2.
Take the square root of 625, which is 25. So, the length of the hypotenuse (last side) is 25m. Add the 7m that is sticking out of the ground, to get 32m.

5 0

3 years ago

Read 2 more answers

What is the GCF for 7x2 + 21?

laiz [17]

Answer:

35

Step-by-step explanation:

7x2+21

14+21

35

*The underlined problems is what you do first*

4 0

3 years ago