solve the simultaneous equation: 5x - 2y=14 and 2x +2y=14. using substitution method
We can solve this simultaneous equation using the substitution method as follows:
1. Rearrange one of the equations to make one of the variables the subject, for example:
2x + 2y = 14
2y = -2x + 14
y = -x + 7
2. Substitute this expression for y into the other equation, and solve for x, for example:
5x - 2y = 14
5x - 2(-x + 7) = 14
5x + 2x - 14 = 14
7x = 28
x = 4
3. Substitute this value of x back into one of the original equations and solve for y, for example:
2x + 2y = 14
2(4) + 2y = 14
8 + 2y = 14
2y = 6
y = 3
So the solution to the simultaneous equation is x=4 and y=3.
To solve a system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation. Let's start with the given system of equations:
Equation 1: 5x - 2y = 14 [Equation A]
Equation 2: 2x + 2y = 14 [Equation B]
Step 1: Solve Equation A for one variable (let's solve it for x):
5x - 2y = 14
5x = 2y + 14
x = (2y + 14) / 5
Now that we have an expression for x in terms of y, we can substitute it into Equation B.
Step 2: Substitute the expression for x in Equation B:
2x + 2y = 14
2((2y + 14) / 5) + 2y = 14
Simplifying:
(4y + 28) / 5 + 2y = 14
Step 3: Multiply every term by 5 to eliminate the fraction:
4y + 28 + 10y = 70
Combine like terms:
14y + 28 = 70
Step 4: Move constant term to the right side:
14y = 70 - 28
14y = 42
Step 5: Solve for y:
y = 42 / 14
y = 3
Now that we have the value for y, we can substitute it back into the expression for x (obtained in Step 1) to find the value of x.
Step 6: Substitute y = 3 into x = (2y + 14) / 5:
x = (2 * 3 + 14) / 5
x = (6 + 14) / 5
x = 20 / 5
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 3.
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation, 2x + 2y = 14, for x:
2x = 14 - 2y
x = (14 - 2y)/2
x = 7 - y
Step 2: Substitute this expression for x into the other equation.
We'll substitute x = 7 - y into the first equation, 5x - 2y = 14:
5(7 - y) - 2y = 14
35 - 5y - 2y = 14
35 - 7y = 14
Step 3: Solve the resulting equation for the remaining variable, y.
-7y = 14 - 35
-7y = -21
y = -21/(-7)
y = 3
Step 4: Substitute the value of y back into either of the original equations to find the value of x.
Let's substitute y = 3 into the second equation, 2x + 2y = 14:
2x + 2(3) = 14
2x + 6 = 14
2x = 14 - 6
2x = 8
x = 8/2
x = 4
The solution to the simultaneous equations 5x - 2y = 14 and 2x + 2y = 14 is x = 4 and y = 3.