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3 years ago

−3x−9y=−12 −3x+7y=4 solve for x

Mathematics

1 answer:

Scrat [10]3 years ago

8 0

Answer:

$\huge{ \boxed{ \boxed{ \sf{ \red{ \sf{x = 1}}}}}}$

Step - by - step explanation :

$\underline{ \underline{ \sf{Solution}}} :$

USING ELIMINATION METHOD :

$\sf{ - 3x - 9y = - 12}$ ••••••• equation ( i )

$\sf{ - 3x + 7y = 4}$ ••••••• equation ( ii )

Subtracting equation ( ii ) from ( i )

Note that while subtracting equation ( ii ) from ( i ) , sign of each term of equation ( ii ) changes and hence becomes 3x - 7y = -4.

$\sf{ \cancel{ - 3x} - 9y = - 12}$

$\sf{ \cancel{3x} - 7y = - 4}$

_____________________

➺ $\sf{ - 16y = - 16}$

➺ $\sf{ \frac{ - 16y}{ - 16} = \frac{ - 16}{ - 16}}$

➺ $\sf{y = 1}$

The value of y is 1. Since , we are asked to find the value of x , substituting the value of y in equation ( i) , we get :

➺ $\sf{ - 3x - 9 \times 1 = - 12}$

➺ $\sf{ - 3x - 9 = - 12}$

➺ $\sf{ - 3x = - 12 + 9}$

➺ $\sf{ - 3x = - 3}$

➺ $\sf{ \frac{ - 3x}{ - 3} = \frac{ - 3}{ - 3}}$

➺ $\sf{ x = \boxed{ \bold{ \red{ \sf{1}}}}}$

Hence , the value of x is 1 .

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☞ $\underline{ \sf{Extra \: Info}} :$

There are many methods to solve such simultaneous equations. They are :

Graphical method : In this method , we find a few pairs of solutions to each of two given equations. The pairs of solutions of each equation are plotted in a graph and by joining them, two separate straight line lines are obtained. The coordinates of the point of intersection of two straight lines are the solutions to the given equation.

Elimination method : In this method, we add or subtract the given equations to eliminate one of the two variable by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.

Substitution method : In this method , a variable is expressed in terms of another variable from one equation and it is substituted in the remaining equations.

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✑ Learn more :

Solve system of equations using elimination method :

brainly.com/question/20160304

What is the substitution method ?

brainly.com/question/15936865

Hope I helped ! ツ

Have a wonderful day / night ♡

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Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.

hram777 [196]

The center of mass is mathematically given as

$\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$

<h3>What is the center of mass.?</h3>

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

$\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end$

We calculate the total mass of the system.

$\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}$

Step 03: Calculate the moment of the system.

$\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}$

we calculate the center of mass.

$\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$