Question

complete the statements about the system of linear equation respresented by the tables the equation respented the left table is

Answer 1

Answer:

The equation representing the left table is

y = 1.5x - 6

The equation representing the right table is

y = -4x + 6.1

The solution to the system of equations is

(2.2, -2.7)

Answer 2

A system of linear equations contains multiple linear equation

• The equation of the left table is $y =1.5x -6$
• The equation of the right table is $y =-4x +6.1$.
• The solution to the system of equations is (2.2,-2.7)

The left table

The slope is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

Using the points on the table, we have:

$m = \frac{-4.5 --6}{1-0}$

$m = \frac{1.5}{1}$

$m = 1.5$

So, the equation is calculated using

$y =m(x -x_1) + y_1$

This gives

$y =1.5(x -0) -6$

Open bracket

$y =1.5x -6$

The right table

The slope is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

Using the points on the table, we have:

$m = \frac{2.1 -6.1}{1-0}$

$m = \frac{-4}{1}$

$m = -4$

So, the equation is calculated using

$y =m(x -x_1) + y_1$

This gives

$y =-4(x -0) +6.1$

Open bracket

$y =-4x +6.1$

The solution

We have:

$y =1.5x -6$

$y =-4x +6.1$

Equate both equations as follows

$-4x + 6.1 = 1.5x - 6$

Collect like terms

$-4x -1.5x = -6.1 - 6$

$-5.5x = -12.1$

Divide both sides by -5.5

$x = 2.2$

Substitute 2.2 for x in $y =1.5x -6$

$y =1.5 \times 2.2 -6$

$y =-2.7$

Hence, the solution to the system of equations is (2.2,-2.7)

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