Question

What is the solution set for this system of equations?

3x + y = 0
x − 6y = 19
please helpppp

Answer 1

Given:-

• 3x + y = 0 ---- eqⁿ ( 1 )
• x - 6y = 19 ---- eqⁿ ( 2 )

Multiply the given eqⁿ ( 1 ) to 6

• 6 ( 3x + y = 0 )
• 18x + 6y = 0 ---- eqⁿ ( 3 )

now , add the eqⁿ ( 3 ) to eqⁿ ( 2 )

18x + 6y = 0

x - 6y = 19

————————

19x = 19

x = 19/19

x = 1

now , put the value of x = 1 in eqⁿ ( 1 )

• 3x + y = 0
• 3( 1 ) + y = 0
• 3 + y = 0
• y = 0-3
• y = -3

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hope it helps! :)

Answer 2

Answer: (x,y) = (1, -3)

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Work Shown:

Solve the first equation for y.

3x+y = 0

y = -3x

Then substitute that into the other equation to solve for x.

x-6y = 19

x-6(-3x) = 19

x+18x = 19

19x = 19

x = 19/19

x = 1

Once we determine x, we can determine y.

3x+y = 0

3*1+y = 0

3+y = 0

y = -3

Or you could say:

x-6y = 19

1-6y = 19

-6y = 19-1

-6y = 18

y = 18/(-6)

y = -3

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In summary we get x = 1 and y = -3 pairing up together.

The ordered pair solution is (x,y) = (1, -3)

To confirm the answer, plug the coordinates back into the original equations. Simplify both sides. You should get the same thing on both sides. I'll let you do these confirmation steps.

Visually you can use something like Desmos or GeoGebra to note that the two lines intersect at (1, -3)