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inna [77]
3 years ago
6

Solve the system of linear equations using multiplication.

Mathematics
2 answers:
Anna71 [15]3 years ago
5 0

Answer:

(8,-1)

Step-by-step explanation:

The given system is:

3x+3y=21

6x+12y=36

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

x+y=7

x+2y=6

We could solve the first equation for x and replace the second x with that.

Let's do that.

x+y=7

Subtract y on both sides:

x=7-y

So we are replacing the second x in the second equation with (7-y) which gives us:

(7-y)+2y=6

7-y+2y=6

7+y=6

y=6-7

y=-1

Now recall the first equation we arranged so that x was the subject. I'm referring to x=7-y.

We can now find x given that y=-1 using the equation x=7-y.

Let's do that.

x=7-y with y=-1:

x=7-(-1)

x=7+1

x=8

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

3x+3y=21 with (x,y)=(8,-1):

3(8)+3(-1)=21

24+(-3)=21

21=21 is a true equation so the "solution" looks promising still.

6x+12y=36 with (x,y)=(8,-1):

6(8)+12(-1)=36

48+(-12)=36

36=36 is also true so the solution has been verified since both equations render true for that point.

nikitadnepr [17]3 years ago
5 0

3x + 3y = 21

6x + 12y = 36

\frac{6x + 12y=36}{6} \\\\x+2y=6\\\\x=6-2y\\----------\\3(6-2y)+3y=21\\\\18-6y+3y=21\\\\18-3y=21\\\\-1(-3y=3)\\\\3y=-3\\\\y=-1

3x+3y=21\\\\3x+3(-1)=21\\3x-3=21\\3x=24\\x=8

x = 8 and y = -1

⭐ Please consider brainliest! ⭐

✉️ If any further questions, inbox me! ✉️

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