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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y=-3x + 7
X
у
Ñ…
y
0
5
-6
9
3
6
-3
8
6
7.
0
7
9
8
3
6
The equation that represents the other equation is y =
X+ .
The solution of the system is (
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10 Type the correct answer in the box Use numerals instead of words If necessary use for the fraction bars A system of linear equations is given by the tables O class=

Respuesta :

JeanaShupp

Answer: The equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .

The solution of the system is (3,6).

Step-by-step explanation:

Linear equation: [tex]y=mx+c[/tex]  , where m= slope

c = y-intercept.

In the first table, the y-intercept = 5     [ y-intercept = value of y at x=0.

Slope for first table  = [tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{6-5}{3-0}=\dfrac{1}{3}[/tex]

The equation that represents the first table:

[tex]y=\dfrac{1}{3}x+5[/tex]

So, the equation that represents the other equation is [tex]y=\dfrac{1}{3}x+5[/tex] .

Also, the solution of the system is the common point (x,y) that satisfy both equations in the system.

Here, x=3 and y=6 is the common value in both tables.

So, the solution of the system is (3,6).

The linear equation of the first table is y = 1 / 3 x + 5

The solution to the system of equation is (3, 6)

Point slope equation;

  • y = mx + b

where

m = slope

b = y-intercept

Therefore, y = - 1 /3 x + 7 is the equation for the second table.

The equation for the first table can be solved using (0, 5)(3, 6) from the table. Therefore,

m = 6 - 5 / 3 - 0 = 1 / 3

let's find b using (0, 5)

5 = 1 / 3(0) + b

b = 5

Therefore, the equation of the first table is as follows:

  • y = 1 / 3 x + 5

The solution to the system of equation can be calculated as follows:

y + 1 /3 x  = 7

y - 1 / 3 x  = 5

2y = 12

y = 12 / 2

y = 6

6 - 1 / 3 x = 5

- 1 / 3 x = 5 - 6

- 1 / 3 x = - 1

x = 3

Therefore, the solution to the system of equation is (3, 6)

learn more on linear equation here: https://brainly.com/question/2263981?referrer=searchResults

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