How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $2x+y=0$ and $5x-y=7$ ?

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $2x+y=0$ and $5x-y=7$ ?

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Answer 1 · 2018-03-07T10:12:34

graph{(2x+y)(5x-y-7)=0 [-10, 10, -5, 5]}
$color(red)(x=1$ $&$ $color(magenta)(y=-2$

Explanation:

$5x-y=7$
$y=5x-7$

Given that, $2x+y=0$

Replacing, $y=5x-7$ in $2x+y=0$

$2x+(5x-7)=0$

$7x-7=0$

$7x=7$

$color(red)(x=1$

Replacing $x=1$ , in $y=5x-7$

$y=5xx1-7$

$color(magenta)(y=-2$

The values are consistent.

Alternatively ,
Consider $y=5x-7$ and plot the points on the graph that satisfy the equation, such as $(0,-7), (2,3)$ etc
and for $2x+y=0$ , you could plot $(0,0), (2,-2)$ etc

You would get two lines in the graph. Mark the point of intersection and that's the solution for the equations.
Here, the lines meet at (1,-2). Therefore the solution is, $x=1, y=-2$ (which matches the answer above:) )

P.S. to get the points to plot on the graph for both the equations, replace $x$ as any value and then get the corresponding value of $y$ from the equality.

~Hope this helps!

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $2x+y=0$ and $5x-y=7$ ?

1 Answer

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 2x+y=02x+y=0 and 5x-y=75x-y=7?

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How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent $2x+y=0$ and $5x-y=7$ ?