How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $3 x - y = 9$ $3x-y=9$ and $2 x + y = 6$ $2x+y=6$ ?

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $3 x - y = 9$ $3x-y=9$ and $2 x + y = 6$ $2x+y=6$ ?

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Answer 1 · 2018-01-08T09:55:58

$(3, 0)$ $(3,0)$

Explanation:

Given -

$3 x - y = 9$ $3x-y=9$ -------------(1)
$2 x + y = 6$ $2x+y=6$ -------------(2)

If the slopes are different, both are consistent, else inconsistent.

When the equations are in the form

$a x + b y = c$ $ax+by =c$
The formula for slope is $m = - \frac{a}{b}$ $m=- a/b$
Slope of the first line $m_{1} = - \frac{3}{- 1} = 3$ $m_1=- 3/(-1)=3$
Slope of the second line $m_{2} = - \frac{2}{1} = 2$ $m_2=- 2/1=2$

The slopes are different. They are consistent.

We have to find the intercepts for the two lines to graph them

y-intercept of the 1st line

$3 (0) - y = 9$ $3(0)-y=9$
$y = - 9$ $y=-9$
$(0, - 9)$ $(0, -9)$

x-intercept of the 1st line

$3 x - (0) = 9$ $3x-(0)=9$
$x = \frac{9}{3} = 3$ $x=9/3=3$
$(3, 0)$ $(3,0)$

y-intercept of the 2nd line

$2 (0) + y = 6$ $2(0)+y=6$
$y = 6$ $y=6$
$(0, 6)$ $(0,6)$

x-intercept of the 2nd line

$2 x + 0 = 6$ $2x+0=6$
$x = \frac{6}{2} = 3$ $x=6/2=3$
$(3, 0)$ $(3, 0)$

[ $(3, 0)$ $(3, 0)$ is a common point for both the lines. Hence it is the solution]

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $3 x - y = 9$ $3x-y=9$ and $2 x + y = 6$ $2x+y=6$ ?

1 Answer

Explanation:

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $3 x - y = 9$ $3x-y=9$ and $2 x + y = 6$ $2x+y=6$ ?