Can you guys help me with this math question?

Question

solve system of equation

5r+2s=0
-3t=12
6s+5t=10

Answer 1

First, you need to find t. So, the second equation is the easiest to find because all you need to do is divide the -3t over 12. If you divide the -3t over 12, the answer for t=-4
Now you know what t is. T = -4

Then you will take the third equation and plug in T. The reason for this is because the first equation does not have a T, so there's no way in plugging it in.

6s+ 5(-4)=10 <-see? i plugged in -4 as t.

6s-20=10 <--this is what you get by multiplying 5(-4)

Add 20 to both sides.

6s-20+20=10+20
The -20 and +20 cancels out.

so you end up with 6s=30
You now divide the 6s and 30
which equals 5. <--just like the beginning we did with the -3=12

Now you know what S is. s = 5.

Now you plug it all in.

S = 5 and T = -4

Now, the first equation is 5r+2s = 0
5r+2(5)= 0<--plug in the S and you don't plug in anything for T because there is no T.

So 5r+10=0.
Now you minus 10 from both side

5r+10-10=-10
The +10 and -10 cancels out again.
You have left 5r=-10
So you divide 5r into -10

The answer is R = -2.

Now you have it.

THE REAL ANSWER IS

R=-2
S=5
T=-4

Try plugging it in and see if it works! =)

Answer 2

To solve this system of equations, lets use the Substitution method.

-3t = 12
t = -4

6s + 5t = 10
6s + 5(-4) = 10
6s = 10 - (-20)
6s = 30
s = 5

5r + 2(5) = 0
5r + 10 = 0
5r = -10
r = -2

ANSWERS: r = -2, s =5 , t = -4

Check the answers
5(-2) + 2(5) = 0
-10 + 10 =0
0 = 0

-3(-4) = 12
12 = 12

6(5) + 5(-4) = 10
30 + (-20) = 10
10 = 10

Answer 3

-3t / (-3) = 12 / (-3)
t = -4

Substitue 4 for t in the third equation:
6s + 5 (-4) = 10
6s - 20 = 10
6s + 20 - 20 = 10 + 20
6s = 30
s = 5

Substitute -5/3 for s in the first equation:
5r + 2 (5) = 0
5r + 10 = 0
5r + +10 - 10 = 0 -10
5r = -10
5r/5 = -10 / 5

r = -2

Answer 4

Take the -3t=12 and solve for t

t=12/-3 thus t=-4

Then plug it in to solve for s like 6s+5(-4)=10
6s+(-20)=10 so 6s=10+20
6s=30 so s=5

Now solve for R with what we know.
5r+2(5)=0 so 5r+10=0
5r=-10 so r=-2

t=-4 s=5 r=-2

Answer 5

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Answer 6

5r+2s=0
-3t=12
6s+5t=10

-3t=12
t=12/-3
t=-4

therefore
6s+5t=10
6s+5(-4)=10
6s-20=10
6s=30
s=5

therefore
5r+2s=0
5r+2*(5)=0
5r+10=0
5r=-10
r=-2

Answer 7

t = - 4

6s - 20 = 10
6s = 30
s = 5

5r + 10 = 0
r = - 2

r = - 2 , s = 5 , t = - 4

Answer 8

need to solve one equation to get the value of one letter, start with the equation that has one unknow variable -3t=12
t=9
plug this value into one of the other equations, use 6s+5t=10 to find the value for s
6s+(5*9)=10
6s+45=10
6s=-35
s=-5
plug this number into the last equation to get r
5r+(2*-5)=0
5r-10=0
r=-2
so
r=-2, s=-5, and t=9

Answer 9

t = -4 so

s = 5 therefore

r = -2

Answer 10

s=-5r/2
t=-4

-30r/2-20=10
-30r=40+20
r=-2
s=5
t=-4