Mathematics, 08.01.2021 14:00, anaroles04

−3x−9y=−12
−3x+7y=4
solve for x

Answers: 2

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answered: xlebrny1215

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

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 :

link

What is the substitution method ?

link

Hope I helped ! ツ

Have a wonderful day / night ♡

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answered: Guest

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.