Can someone help me in these questions 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.

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3 years ago

Find the value of each variable. Write the equation and solve showing ALL the work.

Anit [1.1K]

The angles must add up to 360 degrees, so we can set the sum of the interior angles equal to 360 and solve for x.

106 + 94 + 135 + x + (x + 5) = 360

Combine like terms:

340 + 2x = 360

2x = 20

x = 10

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3 years ago

Area and perimeter of 9cm and 11cm

Law Incorporation [45]

Answer: Area: 99cm Perimeter: 40cm

Step-by-step explanation:

To find the area, you would multiply 9cm by 11cm because the formula for area is length times width. To find the perimeter, you add all the sides, which would mean you add 9 + 9 + 11 + 11, making the perimeter 40cm.

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CAN SOMEONE HELP ME ASAP THANK YOU SO MUCH :{

Strike441 [17]

I think your answer would be A. AB

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il63 [147K]

People see what they expect to see.

-ur local skatergirl:)

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