Evaluate y4 + 2x When x =1, y = 7

without building the graph, find the coordinates of the point of intersection of the lines given by the equation y=3x-1 and 3x+y

DaniilM [7]

<h2><u>1. Determining the value of x and y:</u></h2>

Given equation(s):

$y = 3x - 1$
$3x + y = -7$

To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.

<h3 /><h3><u>Method-1: Substitution method</u></h3>

Given value of the y-variable: 3x - 1

Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.

$\implies 3x + y = -7$

$\implies3x + (3x - 1) = -7$

$\implies3x + 3x - 1 = -7$

Combine like terms as needed;

$\implies 3x + 3x - 1 = -7$

$\implies 6x - 1 = -7$

Add 1 to both sides of the equation;

$\implies 6x - 1 + 1 = -7 + 1$

$\implies 6x = -6$

Divide 6 to both sides of the equation;

$\implies \dfrac{6x}{6} = \dfrac{-6}{6}$

$\implies x = -1$

Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.

$\implies y = 3(-1) - 1$

$\implies$ $\ \ = -3 - 1$

$\implies$ $= -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h3 /><h3><u>Method 2: System of equations</u></h3>

Convert the equations into slope intercept form;

$\implies\left \{ {{y = 3x - 1} \atop {3x + y = -7}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {y = -3x - 7}} \right.$

Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.

$\implies \left \{ {{y = 3x - 1 } \atop {- (y = -3x - 7)}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.

$\implies\left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

$\implies 0 = (6x) + (6)$

$\implies0 = 6x + 6$

This problem is now an algebraic problem. Isolate "x" to determine its value.

$\implies 0 - 6 = 6x + 6 - 6$

$\implies -6 = 6x$

$\implies -1 = x$

Like done in method 1, substitute the value of x into the first equation to determine the value of y.

$\implies y = 3(-1) - 1$

$\implies y = -3 - 1$

$\implies y = -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h2><u>2. Determining the intersection point;</u></h2>

The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.

⇒ (x, y) ⇒ (-1, -4)

Therefore, the point of intersection is (-1, -4).

<h3>Graph:</h3>

5 0

2 years ago

What is the first step to solve this equation: -3x + 11 = 44

Verdich [7]

You subtract the 11 from both sides, then you get -3x = 33. Next, you divide -3 from both sides, and you get x= -11

7 0

4 years ago

Another one I need help in asap

Paha777 [63]

Answer:

Gold : total

35 : 103

Step-by-step explanation:

USA gold = 35

Total usa = 103

Gold : total

35 : 103

4 0

3 years ago

Which property is shown below?

ElenaW [278]

Answer:

C

Step-by-step explanation:

5+2y+3z=5+3z+2yA

Intercambie los lados para que todos los términos de las variables estén en el lado izquierdo.

5+3z+2yA=5+2y+3z

Resta 5 en los dos lados.

3z+2yA=5+2y+3z−5

Resta 5 de 5 para obtener 0.

3z+2yA=2y+3z

Resta 3z en los dos lados.

2yA=2y+3z−3z

Combina 3z y −3z para obtener 0.

2yA=2y

Anula 2 en ambos lados.

yA=y

Divide los dos lados por y.

y

yA

=

y

Al dividir por y, se deshace la multiplicación por y.

A=

y

Divide y por y.

A=1

6 0

3 years ago

Triangle DABC is similar to DEFG.

lyudmila [28]

Answer:

is there an image provided?

Step-by-step explanation:

7 0

3 years ago

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