Y=-1/2x+6 y=3x-1
To find the point of intersection between the two lines represented by the equations y = -1/2x + 6 and y = 3x - 1, we can set the expressions for y equal to each other and solve for x:
-1/2x + 6 = 3x - 1
To simplify, let's multiply through by 2 to get rid of the fraction:
-1x + 12 = 6x - 2
Combine like terms:
-3x + 12 = -2
Subtract 12 from both sides of the equation:
-3x = -14
Divide by -3:
x = 14/3
Now that we have the x-coordinate, we can substitute it back into one of the original equations to find the corresponding y-coordinate. Let's use y = -1/2x + 6:
y = -1/2(14/3) + 6
y = -7/3 + 6
y = -7/3 + 18/3
y = 11/3
Therefore, the point of intersection of the two lines is (14/3, 11/3).
To find the solution to the equations Y = (-1/2)x + 6 and Y = 3x - 1, you can set the two equations equal to each other and solve for x.
(-1/2)x + 6 = 3x - 1
First, let's get rid of the fractions by multiplying the entire equation by 2 to clear the fraction:
2*(-1/2)x + 2*6 = 2*3x - 2*1
This simplifies to:
-1x + 12 = 6x - 2
Next, let's group the terms with x on one side:
-1x - 6x = -2 - 12
This simplifies to:
-7x = -14
Next, divide both sides of the equation by -7 to solve for x:
x = -14 / -7
Simplifying this gives:
x = 2
Now that we have x = 2, we can substitute this value into either of the equations to solve for y. Let's use the second equation Y = 3x - 1:
Y = 3 * 2 - 1
Simplifying this gives:
Y = 6 - 1
Y = 5
Therefore, the solution to the system of equations is x = 2 and y = 5.
To find the solution to this system of equations, we need to determine the values of x and y that satisfy both equations simultaneously.
The given system of equations is:
y = -1/2x + 6 ... Equation 1
y = 3x - 1 ... Equation 2
To solve the system, we can set the right-hand sides of the two equations equal to each other since they both equal y:
-1/2x + 6 = 3x - 1
Next, we can solve for x by isolating the variable terms:
-1/2x - 3x = -1 - 6
(-1/2 - 6)x = -7
(-13/2)x = -7
Now, we can solve for x by multiplying both sides of the equation by the reciprocal of -13/2, which is -2/13:
x = (-7) * (-2/13)
x = 14/13
Now that we have the value of x, we can substitute it back into either equation to solve for y. Let's use Equation 1:
y = -1/2 * (14/13) + 6
y = -7/13 + 78/13
y = 71/13
Therefore, the solution to the system of equations is x = 14/13 and y = 71/13.