Quick help with algebra problem

solve the system of equations.


4x - 5y = 27
3x - 9y = 36


can you guys show me every step on how to the solve this math problem please...

(4x-5y=27) x 3
(3x-9y=36) x 4

12x-15y=81
12x-36y=144

-21y=63

Y=-3

3x-9(-3)=36
3x-(-27)=36
3x=9

X=3
Y=-3

You can use substitution to solve this, and so you want to get one of the variables by itself and then plug that back into the other equation.

4x = 27 + 5y
x = 27/4 + 5/4y

3(27/4 + 5/4y) - 9y = 36
81/4 + 15/4y - 9y = 36
81/4 - 21/4y = 36
-21/4y = 63/4
y=-3

Now that you have a number for y, you can plug that back into the equation.

4x - 5(-3) = 27
4x + 15 = 27
4x=12
x=3

You can then check your answer by putting that x into the other equation, and it should give you what you have for y.

3(3) - 9y =36
9 - 9y = 36
-9y = 27
y = -3

Therefore, the point of intersection is (3,-3).

4x - 5y = 27
3x - 9y =36

Take the second equation, 3x - 9y =36, this can be written as

3x = 36+9y, x = (36+9y)/3

X = 12+3y

Now substitute the above value of X in 4x - 5y = 27

4*(12+3y) - 5y = 27

48 + 12y - 5y =27
7y = 27-48, 7y = -21, y=-21/7

y = -3;

Now substitute y=-3 in x=12+3y;

x = 12 +(3*-3)
x = 12+(-9)
X= 12-9
X= 3

hence the solution of the pair of equations is X=3 Y= - 3

multiply the top equation by 3 and the bottom equation by 4 .

12x - 15y = 81
12x - 36y = 144 Now SUBTRACT the TWO equations by changing the second equations's signs to the their opposites then adding.

12x - 15y = 81
-12x -+36y = -144

21y = -63

y = -3 can you find x now?

4x - 5y = 27
3x - 9y = 36

Multiply second equation by 4/3

4x - 5y = 27
4x - 12y = 48

Subtract

7y = -21
y = -3

Plug y back into one of the earlier equations and solve for x
4x - 5y = 27
4x - 5(-3) = 27
x = 3

4x - 5y = 27 ------- (1)
3x - 9y = 36 ------- (2)

(1) × 3 and (2) × 4
12x - 15y = 81 ------- (3)
12x - 36y = 144 ------- (4)

(3) – (4)
21y = – 63
y = – 3

using
4x - 5y = 27 ------- (1)
4x + 15 = 27
4x = 12
x = 3
----

4x - 5y = 27 -(1)
3x - 9y = 36 -(2)

from (2), x - 3y = 12 -(3)

from (3), 4x - 12y = 48 -(4)

(4) - (1), get y= -3

put y= -3 into (3) and get x=3

Answer is: x=3 and y= -3