Can I please have help as to how to solve a system using substitution? I have a quiz coming up and I want to ace it. :) Thank you.
@Ms.Sue could you please help me?
If you are asked to use substitution, usually one of the equations has a variable with coefficient of 1
e.g. 3x + y = 8
solve that equation for y (or x) and sub it into the other equation.
e.g.
5x - 7y = 59
x + 4y = 1
from the 2nd, notice that the x term has a coefficient of 1, so solve for x
x = 1 -4y
plug that into the other equation:
5(1-4y) - 7y = 59
5 - 20y - 7y = 59
-27y = 54
y = -2
now back into x = 1 - 4y
x = 1 -4(-2) = 9
x = 9, y = -2
Of course, I can help you solve a system of equations using the substitution method! Let's go through the steps together.
Step 1: Solve one of the equations for one variable in terms of the other variable.
- Choose one equation and isolate one variable on one side of the equation.
Step 2: Substitute the expression from Step 1 into the other equation.
- Take the expression you obtained in Step 1 and substitute it for the corresponding variable in the other equation.
Step 3: Solve the resulting equation for the remaining variable.
- Simplify and solve the equation you obtained from Step 2. This will give you the value of one variable.
Step 4: Substitute the value obtained in Step 3 back into one of the original equations to solve for the other variable.
- Take the value you obtained in Step 3 and substitute it back into either of the original equations. This will give you the value of the second variable.
Step 5: Check your solution by substituting the values of the variables back into both original equations.
- Substitute the values of the variables into each of the original equations and ensure that both equations are true.
By following these steps, you'll be able to solve a system of equations using the substitution method. Remember to take your time, pay attention to detail, and double-check your answers to avoid any mistakes. Good luck on your quiz! If you have any specific equations you'd like me to guide you through, please feel free to share them.