6x+8y=4
8x-3y=19
48x+64y=32
-48x+82y=-14
82=-82
y=-1
6x+8y=4
6x+8(-1)=4
6x-8=4
6x=4-8
6x=12
X=2
Correct answer.
But
82=-82 Isn't correct.
Least Common Denominator of 6 and 8 is 24, not 48.
6 x + 8 y = 4 Multiply both sides by 4
24 x + 32 y = 16
8 x - 3 y = 19 Multiply both sides by - 3
- 24 x + 9 y = - 57
24 x + 32 y = 16
+
- 24 x + 9 y = - 57
___________________
41 y = - 41
y = - 1
6 x + 8 y = 4
6 x + 8 * ( - 1 ) = 4
6 x - 8 = 4
6 x = 4 + 8
6 x = 12
x = 2
82y=-82
To solve this system of equations, you can use the method of substitution or elimination. I will explain the process using the method of substitution.
1. Start by solving one equation for one variable in terms of the other variable. Let's solve the first equation for x:
6x + 8y = 4
Subtract 8y from both sides:
6x = 4 - 8y
Divide both sides by 6:
x = (4 - 8y) / 6
2. Substitute the expression for x from the first equation into the second equation:
8x - 3y = 19
Replace x with (4 - 8y) / 6:
8((4 - 8y) / 6) - 3y = 19
Simplify the equation:
(32 - 64y) / 6 - 3y = 19
Multiply both sides by 6 to get rid of the fraction:
32 - 64y - 18y = 114
Combine like terms:
-82y + 32 = 114
Subtract 32 from both sides:
-82y = 82
Divide both sides by -82:
y = -1
3. Now that we have the value of y, substitute it back into the expression for x in the first equation:
x = (4 - 8(-1)) / 6
Simplify the equation:
x = 12 / 6
x = 2
4. The solution to the system of equations is x = 2 and y = -1.