Final answer:
To solve a system of equations by elimination using a calculator, follow the steps of identifying the unknowns, solving for one unknown, substituting and eliminating terms, simplifying, using the calculator to find the value of the unknown, substituting back, and checking the solution.
Step-by-step explanation:
To solve a system of equations by elimination using a calculator, follow these steps:
- Identify the unknowns (variables) in the system of equations.
- Choose one equation and solve for one of the unknowns in terms of the other unknown(s).
- Substitute the expression found in step 2 into the other equation(s) in the system.
- Eliminate terms with the same unknown by adding or subtracting the equations.
- Continue to simplify the equations by eliminating terms until you are left with one equation with one unknown.
- Use your calculator to solve the equation and find the value of the unknown.
- Substitute the value found in step 6 back into one of the original equations to solve for the other unknown(s).
- Check your solution by substituting the values into both equations in the system.
For example, let's solve the following system of equations using elimination:
Equation 1: 2x + 3y = 8
Equation 2: 4x - y = 5
Start by choosing one equation and solving for one of the unknowns:
Let's solve Equation 1 for x:
2x = 8 - 3y
x = 4 - 1.5y
Now, substitute this expression for x into Equation 2:
4(4 - 1.5y) - y = 5
16 - 6y - y = 5
15 - 7y = 5
-7y = -10
y = 1.43
Substitute the value of y back into the expression for x:
x = 4 - 1.5(1.43)
x = 4 - 2.145
x = 1.855
The solution to the system of equations is x = 1.855 and y = 1.43.