System of equations Help please Asap Show work !

5. 3x + 2y = 24
15x - 2y = 48

6. x - 6 = 3y
2(3y - 6) = 5x


PLease show work thanks !!!! each problem

5. 3x + 2y = 24
15x - 2y = 48

Add the two equations to get:

18x = 72
x = 72 / 18 divide each side by 18
x = 4

Substitute 4 for x in either equation. I'll do it in the first:
3(4) + 2y = 24
12 + 2y = 24
2y = 24 - 12 subtract 12 from each side
2y = 12 calculate the right side
y = 12 / 2 divide each side by 2
y = 6 calculate the right side

6. x - 6 = 3y
2(3y - 6) = 5x

Since x - 6 = 3y,
x = 3y + 6 add six to each side
now substitute 3y + 6 for x in the second formula, to get:
2(3y - 6) = 5(3y + 6)
6y - 12 = 15y + 30 multiply the terms inside parentheses by the factors outside
-12 = 15y + 30 - 6y subtract 6y from each side
-12 - 30 = 15y - 6y subtract 30 from each side
-18 = 9y subtract similar terms on each side
-18 / 9 = y divide each side by 9
-2 = y calculate the left side
y = -2 by symmetry

Now substitute -2 for y in the (recast) first equation, to get:
x = 3(-2) + 6
x = -6 + 6
x = 0

The method that I used for problem 5 is known as the elimination method. The method that I used for problem 6 is known as the substitution method.

3x + 2y = 24
15x - 2y = 48
cancel out the y's and add the x's and natural numbers.
18x = 72 x = 4
take one equation and replace x with 4
3(4) + 2y = 24
12 + 2y = 24
2y = 12
y = 6




rewrite it first

x - 3y = 6
-5x + 6y = 12 (simplify)

2( x - 3y ) = 6 must make y's equal so you can cancel them out.

2x - 6y = 6
-5x + 6y = 12

-3x = 18
x = -6

plug x into one of the equations to get y
(-6) - 3y = 6
-3y = 12
y = -4