Solving Linear Equations: 2x = 5y + 4 and 3x - 2y + 16 = 0 by Elimination Method
In this article, we will learn how to solve a system of linear equations using the elimination method. The system of equations we will be solving is:
Equation 1: 2x = 5y + 4 Equation 2: 3x - 2y + 16 = 0
Step 1: Write the equations in standard form
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. Let's rewrite the given equations in standard form:
Equation 1: 2x - 5y = -4 Equation 2: 3x - 2y = -16
Step 2: Make the coefficients of y's opposite
To eliminate the y-variable, we need to make the coefficients of y's opposite in both equations. We can do this by multiplying Equation 1 by 2 and Equation 2 by 5:
Equation 1: 4x - 10y = -8 Equation 2: 15x - 10y = -80
Step 3: Add the equations to eliminate y
Now that the coefficients of y's are opposite, we can add the two equations to eliminate y:
(4x - 10y = -8) + (15x - 10y = -80)
19x = -68
Step 4: Solve for x
Now that we have a single equation with one variable, we can solve for x:
x = -68/19 x = -4
Step 5: Substitute x into one of the original equations to solve for y
Now that we have the value of x, we can substitute it into one of the original equations to solve for y. We will use Equation 1:
2x - 5y = -4 2(-4) - 5y = -4 -8 - 5y = -4 -5y = 4 y = -4/5 y = -0.8
Solution
Therefore, the solution to the system of linear equations is x = -4 and y = -0.8.
By using the elimination method, we were able to solve the system of linear equations 2x = 5y + 4 and 3x - 2y + 16 = 0.
