How many solutions does the system of equations have? 6x+y=2 -18x+3y=12

2 answers:

6 0

There will be one solution. To solve that:
1. Get the y alone by switching the places.
6x+y=2 > y=2-6x
-18x+3y=12 > 3y=12-18x > Then divide 3 on each number > y=4-6x
After doing that, you can solve this in graphing or algebra way.

Ima do the algebra way:

SO we have 2 system of equations. Now pick one equestion.
I will pick, y=2-6x. Now Ima replace the Y with the other equation y=4-6x >
4-6x=2-6x.

Now solve. And get > 0 aka Infinite Solution.

kenny6666 [7]3 years ago

6 0

See if they are paralell, if they are, there are no solutions
thn see if they are the same line, if they are, there is infinite soutions

so

6x+1y=2
-18x+3y=12
divide 2nd equation by -3
6x-y=4

compare
6x+y=2 and
6x-y=4
they are actually perpenduclar
mean 1 soltuions

if yo wantedsoltion
add

6x+y=2
<u>6x-y=4 +</u>
12x+0y=6
12x=6
x=1/2

6x+y=2
6(1/2)+y=2
3+y=2
y=-1

x=1/2
y=-1
(1/2,-1)
1 soluiton

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Writing the slope-intercept form of a linear equation, we have:

$y=mx+b$

Where m is the slope and b is the y-intercept.

Since parallel lines have the same slope, we can see that the slope of the line y = 2/3x + 1 is equal m = 2/3, so for our equation we also have m = 2/3.

Now, using the point (0, -4), we have:

$\begin{gathered} y=\frac{2}{3}x+b \\ (0,-4)\colon \\ -4=\frac{2}{3}\cdot0+b \\ b+0=-4 \\ b=-4 \end{gathered}$

So our equation is:

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Mazyrski [523]

Answer:

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Y-Intercept: $(0,-5)$

Step-by-step explanation:

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