3x-14y=O and x-4y+1=0
3x = 14y
x = 14y/3
x-4y+1=0
Substitute 14y/3 for x in the third equation and solve for y. Insert that value into the first equation to solve for x. Check by putting both values into the second equation.
To solve the system of equations, we can use either substitution or elimination method. Let's use the elimination method.
Given the equations:
1) 3x - 14y = 0
2) x - 4y + 1 = 0
To eliminate one variable, we can multiply the equations by certain numbers so that when we add or subtract them, one of the variables is eliminated.
First, let's eliminate the "x" variable by multiplying equation 2)
by 3:
3 * (x - 4y + 1) = 0
3x - 12y + 3 = 0
Now, we can subtract this result from equation 1) in order to eliminate the "x" variable:
(3x - 14y) - (3x - 12y + 3) = 0
3x - 14y - 3x + 12y - 3 = 0
Simplifying the equation, we have:
-14y + 12y - 3 = 0
-2y - 3 = 0
Now, let's solve for "y":
-2y - 3 = 0
-2y = 3
y = 3/(-2)
y = -3/2
We have found the value of "y" as -3/2.
To find the value of "x," we substitute the value of "y" back into one of the original equations. Let's use equation 1):
3x - 14(-3/2) = 0
3x + 21 = 0
3x = -21
x = -21/3
x = -7
Therefore, the solution to the system of equations is x = -7 and y = -3/2.