y=1/2x-3
y=3/2x-1
y = 1/2x - 3
1/2x = 3
x = 6
y = 3/2x - 1
3/2x = 1
x = 2/3
To find the solution to the system of equations:
1. Start by setting the two equations equal to each other, since both equations are equal to y:
1/2x - 3 = 3/2x - 1
2. Get rid of the fractions by multiplying everything by the least common denominator, which in this case is 2. Multiply both sides of the equation by 2:
2 * (1/2x - 3) = 2 * (3/2x - 1)
This simplifies to:
x - 6 = 3x - 2
3. Next, combine like terms. Subtract x from both sides:
x - x - 6 = 3x - x - 2
-6 = 2x - 2
4. Add 2 to both sides of the equation:
-6 + 2 = 2x - 2 + 2
-4 = 2x
5. Divide both sides by 2 to solve for x:
-4/2 = 2x/2
-2 = x
So, the value of x is -2.
6. Now that we have x, we can substitute this value back into one of the original equations to find y. Let's use the first equation y = 1/2x - 3:
y = 1/2(-2) - 3
y = -1 - 3
y = -4
So, the solution to the system of equations is x = -2 and y = -4.