How can (1/4)x-3=(1/2)x+8 be setup as a system of equations?
4y + 4x = −12
2y + 2x = 16
4y − x = −12
2y − x = 16
4y + x = −12
2y + x = 16
4y − 4x = −12
2y − 2x = 16
To set up the given equation, (1/4)x - 3 = (1/2)x + 8, as a system of equations, we need to isolate the variable on one side of the equation.
To do this, we can multiply both sides of the equation by a common denominator, in this case, 4, to eliminate the fractions.
Multiplying both sides of the equation by 4, we get:
4 * ((1/4)x - 3) = 4 * ((1/2)x + 8)
x - 12 = 2x + 32
Now, we can rewrite the equation in standard form by moving all terms to one side:
x - 2x = 32 + 12
-x = 44
Dividing both sides by -1, we get:
x = -44
Now, we can substitute this value of x back into the original equation to solve for y:
(1/4)(-44) - 3 = (1/2)(-44) + 8
Simplifying the equation, we get:
-11 - 3 = -22 + 8
-14 = -14
Therefore, the solution is x = -44 and y = -14.
Why make things complicated ?
Just solve it ....
(1/4)x-3=(1/2)x+8
times 4, the LCD
x - 12 = 2x + 32
-x = 44
x = -44
Where does y come from in the pairs of equations?