Solve the simultaneous equations: 3X−14Y=0 and X−4Y+1=0
the 2nd equation says that x = 4y-1
So, using that in the first equation,
3(4y-1) - 14y = 0
12y-3 - 14y = 0
-2y = 3
y = -3/2
so, x = 4y-1 = -7
Lindo
To solve the simultaneous equations, we'll use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other.
Let's solve the second equation for X:
X - 4Y + 1 = 0
Rearranging the equation, we have:
X = 4Y - 1
Step 2: Substitute the expression we found for X into the other equation.
Now, substitute X = 4Y - 1 into the first equation:
3(4Y - 1) - 14Y = 0
Expanding and simplifying, we get:
12Y - 3 - 14Y = 0
-2Y - 3 = 0
Step 3: Solve for Y.
Adding 3 to both sides of the equation:
-2Y = 3
Divide both sides by -2:
Y = -3/2
Step 4: Substitute the value of Y we found into one of the original equations to solve for X.
Let's substitute Y = -3/2 into the second equation:
X - 4(-3/2) + 1 = 0
Simplifying, we have:
X + 6 - 4/2 + 1 = 0
X + 6 - 2 + 1 = 0
X + 5 = 0
Subtracting 5 from both sides:
X = -5
So the solution to the simultaneous equations is X = -5 and Y = -3/2.