Systems of linear equations worksheet substitution is a method used to solve a system of equations by isolating one variable in one of the equations and substituting it into the other equation. This method is particularly useful when solving systems of equations with two variables.
By using substitution, we can find the values of the variables that satisfy both equations in the system. This method is often preferred when one of the equations is already solved for one of the variables, making it easier to substitute into the other equation.
Example of Systems of Linear Equations Worksheet Substitution
Let’s consider a system of equations:
2x + y = 10
3x – y = 2
First, we can solve the first equation for y:
y = 10 – 2x
Next, we substitute this expression for y into the second equation:
3x – (10 – 2x) = 2
3x – 10 + 2x = 2
5x – 10 = 2
5x = 12
x = 2.4
Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:
2(2.4) + y = 10
4.8 + y = 10
y = 5.2
Therefore, the solution to the system of equations is x = 2.4 and y = 5.2.
Systems of linear equations worksheet substitution is a powerful tool for solving systems of equations efficiently and accurately. By isolating variables and substituting them into other equations, we can easily determine the values that satisfy both equations in the system.