How do you solve an eguation with 2 variables?
You have to have two independent equations to solve for each of the variables.
To solve a system of equations with two variables, you need to have two separate equations that are independent of each other. These equations should involve the same variables. By solving the system of equations, you can determine the values of the variables.
Here's a step-by-step method to solve a system of equations with two variables:
1. Write down the two equations. For example, let's say we have the following system of equations:
Equation 1: 2x + 3y = 10
Equation 2: 4x - 2y = 5
2. Choose one of the equations and solve it for one of the variables. Since it's up to you which equation to choose, you may choose the one that seems easier to work with. Let's solve Equation 1 for x:
2x + 3y = 10
2x = 10 - 3y
x = (10 - 3y)/2
3. Substitute the expression you found for x into the other equation. Use parentheses to indicate the substitution clearly. Let's substitute the expression for x into Equation 2:
4((10 - 3y)/2) - 2y = 5
Simplify the equation by performing the necessary calculations:
(20 - 6y) - 2y = 5
20 - 6y - 2y = 5
20 - 8y = 5
4. Solve the resulting equation for the remaining variable. In this case, we're solving for y:
20 - 8y = 5
-8y = 5 - 20
-8y = -15
y = (-15)/(-8)
y = 15/8 or 1.875
5. Substitute the value you found for y back into one of the original equations to solve for the remaining variable. Let's use Equation 1:
2x + 3(1.875) = 10
2x + 5.625 = 10
2x = 4.375
x = 4.375/2
x = 2.1875
6. Check your solution by substituting the values you found for x and y into the other equation. If the left side of the equation equals the right side, then your solution is correct. Let's use Equation 2:
4(2.1875) - 2(1.875) = 5
8.75 - 3.75 = 5
5 = 5
Therefore, the solution to the system of equations is x = 2.1875 and y = 1.875.