There is a pair of x and y values that make each equation true in this system of equations

Mathematics

1 answer:

MAXImum [283]3 years ago

5 0

Given Equations

5x+3y=8--(1)
4x+7y=34--(2)

Let it has solution (x,y)

Add both

$\\ \sf\longmapsto 5x+4x+3y+7y=8+34$

$\\ \sf\longmapsto 9x+10y=42$

It will also have same solution (x,y)

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If two points known on the line AB in the coordinate plane is (7,15) and (18,42), calculate the following..

Ksju [112]

Answer:

Slope = 27/11
AB = 29.15 u

Step-by-step explanation:

Given :-

Two points are given to us .
The points are A(7,15) and B(18,42)

To Find :-

The slope of the line .
The length of line AB .

We can find the slope of the line passing through the points $( x_1,y_1)$ and $( x_2,y_2)$ as ,

$\implies m = \dfrac{ y_2-y_1}{x_2-x_{1}}$

Plug in the respective values ,

$\implies m = \dfrac{ 42-15}{18-7} \\\\\implies \boxed{ m = \dfrac{ 27}{11 }}$

Hence the slope of the line is 27/11 .

$\rule{200}2$

Finding the length of AB :-

We can find the distance between them by using the Distance Formula .

$\implies Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2} \\\\\implies Distance =\sqrt{ (18-7)^2+(42-15)^2 } \\\\\implies Distance =\sqrt{ 11^2 + 27^2 } \\\\\implies Distance =\sqrt{ 121 + 729 } \\\\\implies Distance = \sqrt{ 850} \\\\\implies \boxed{ Distance = 29.15 \ units }$