Algebra 2 help. (10 pts best answer)?

Question

solve the folowing equations algebraically.

a.

5x-y=5

3x-5y=-63

b.

a-b+3c=-8

2b-c=15

3a+2c=-7

Answer 1

5x-y = 5 this will be 25x-5y = 25  reduce the second equation from this you will get  22 x = 38  now put this value in any equation u will the value of y..

Solve the other one similiar..

IITian College

Answer 2

a. Solve for either x or y. I'll solve for y: -y=5-5x       y=5x-5

Then using the substitution method, plug this new equation ^ into the other one for y. sooo

3x-5(5x-5)=-63  

and simplify: 3x-25x+25=-63

                   -22x= -88

                        x= 4

Then plug this back into the first one to solve for y. y=5(4)-5=15

So x=4 and y=15

You can do similar sorts of things for b. Just have to do more work.

Answer 3

Also, it's a good point to always substitute your answers back into all the equations as a double check for your solution

Answer 4

what is wrong with above answer: multiplied first expression by 5, not -5. The y terms do not cancel this way; in fact, they double

a)

solve first equation for y:

   5x-5=y

substitute "5x-5" for y in second equation:

   3x-5(5x-5)=-63

   3x-25x+25=-63

   -22x=-88

   x=4

substitute "4" for x in first equation

   5(4)-y=5

   20-y=5

   y=15

answer: (4,15)

B: similar to A

Answer 5

I do b. and you do a.yourself.

b. Write,

a-b+3c=-8-----(1)

2b-c=15--------(2)

3a-2c=-7-------(3)

chang (2) as

b=(15+c)/2 and put it in (1) so that (1) becomes

2a+5c=-1------(4)

2*(4)+5*(3) get

a=-37/19-------(5)

from (4),(5) get

2(-37/19)+5c=-1=>

c=11/19--------(6)

from (1),(5),(6) get

b=148/19

So, a=-37/19,b=148/19 & c=11/19

Answer 6

Problem A:

5x - y = 5

y = 5x - 5

3x - 5y = - 63

5y = 3x + 63

y = (3x + 63)/5

Value of x:

5(5x - 5) = 3x + 63

25x - 25 = 3x + 63

22x = 88

x = 4

Value of y:

= 5(4) - 5

= 20 - 5

= 15

Answer: x = 4, y = 15

Proof (1st equation):

5(4) - 15 = 5

20 - 15 = 5

Proof (2nd equation):

3(4) - 5(15) = - 63

12 - 75 = - 63

Problem B:

a - b + 3c = - 8

b = a + 3c + 8

2b - c = 15

2(a + 3c + 8) - c = 15

2a + 6c + 16 - c = 15

5c = - 2a - 1

c = - 0.4a - 0.2

3a + 2c = - 7

3a + 2(- 0.4a - 0.2) = - 7

3a - 0.8a - 0.4 = - 7

2.2a = - 6.6

a = - 3

c = - 0.4(- 3) - 0.2

c = 1.2 - 0.2

c = 1

b = - 3 + 3(1) + 8

b = - 3 + 3 + 8

b = 8

Answer: a = - 3, b = 8, c = 1

Proof (1st equation):

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

- 11 + 3 = - 8

- 8 = - 8

Proof (2nd equation):

2(8) - 1 = 15

16 - 1 = 15

15 = 15

Proof (3rd equation):

3(- 3) + 2(1) = - 7

- 9 + 2 = - 7

- 7 = - 7

Answer 7

1 mult 1st eqn by 5 and subtract wqn 2 from it

25x - 5y =25

-3x + 5y = 63

-------------------

22x       = 88

  x        = 4

put this value in 1st eqn

20 - y =5

     -y=-15

      y=15

b

2b-c =15  b= (c+15)/2

3a+2c=7  a=(-7-2c)/3

a-b+3c = (-7-2c)/3 - (c+15)/2 +3c=8

rationalise denominator

2(-7-2c) - 3(c+15) + 18c = -48

-14-4c -3c -45 +18 c=-48

11c=-48+45+14=11, c=1

putting this value 2b-c=15, 2b-1=15, 2b=16,b=8

3a +2c=-7 3a+2=-7 3a +2=-7,3a=-9,a=-3

Answer 8

What grade and math class are you in???

Answer 9

a) Multiply so that one variable cancels out. In this case, I'm multiplying the top equation by 5 & the bottom equation by -1.

25x-5y=25

-3x+5y=63

Add these up.

22x=88

Divide by the coefficient.

x=4

Substitute this variable in both equations. If y is the same in both of them, you are correct.

20-y=5

-y=-15

y=15

12-5y=-63

-5y=-75

y=15

The answer is (4, 15).

b) This is where it becomes more difficult. I'm going to solve it by a combination of elimination & substitution. Isolate a variable in one equation. In this case, it'll be a in the first one.

a=b-3c-8

Substitute this in for a in the third equation.

3(b-3c-8)+2c=-7

Distribute & combine like terms.

3b-9c-24+2c=-7

3b-7c=17

Now I'm going to take the second equation, which has the same variables, & use substitution.

3(2b-c=15)

-2(3b-7c=17)

6b-3c=45

-6b+14c=-34

11c=11

c=1

Substitute the new value in for c in the original second & third equations.

3a+2=-7

3a=-9

a=-3

2b-1=15

2b=16

b=8

Check this in the first equation, which has all the variables.

-3-8+3=-11+3=-8

The answer is (-3, 8, 1)