y=2x-1 y=3x-2
2x-1=3x-2
add one on both sides
2x=3x-1
subtract 3x on both sides
-x=-1
x=1
To solve the system of equations y = 2x - 1 and y = 3x - 2, we can use the substitution method. This involves solving one equation for one variable and then substituting that value into the other equation. Here are the steps to solve this system:
Step 1: Solve one equation for one variable.
Let's solve the first equation, y = 2x - 1, for y:
y = 2x - 1
Step 2: Substitute this expression for y into the other equation.
Substitute the expression 2x - 1 for y in the second equation, y = 3x - 2:
2x - 1 = 3x - 2
Step 3: Simplify and solve for x.
Subtract 2x from both sides of the equation:
-1 = x - 2
Add 2 to both sides of the equation:
1 = x
So, we have found the value of x, which is 1.
Step 4: Substitute the value of x into one of the original equations to find the corresponding value of y.
Let's substitute x = 1 into the first equation, y = 2x - 1:
y = 2(1) - 1
y = 2 - 1
y = 1
Therefore, the solution to the system of equations y = 2x - 1 and y = 3x - 2 is x = 1 and y = 1.
To find the solution to the system of equations, you can solve them simultaneously by setting the two equations equal to each other:
2x - 1 = 3x -2
To isolate the x term, you can subtract 2x from both sides:
-1 = x - 2
Next, you can add 2 to both sides:
1 = x
Now that you have found the value of x, you can substitute it back into either of the original equations to find the value of y. Let's substitute it into the first equation:
y = 2(1) - 1
y = 2 - 1
y = 1
Therefore, the solution to the system of equations is x = 1 and y = 1.