Solving a System of Equations by Substitution

TL;DR

Learn how to solve a system of equations using the substitution method, demonstrated through an example.

Transcript

okay we're going to solve this system equations and as we can see for the second equation we have the y being isolated for us already right we know exactly why it's equal to negative 3x minus 1. so nice isn't it therefore we should just use the substitution because now i can just plug in this expression here negative 3x minus 1 to the y in the firs... Read More

Key Insights

• ❓ The substitution method is useful for solving systems of equations when one variable can be easily isolated in one of the equations.
• 🍉 Combining like terms before solving the equation helps simplify the problem.
• 😑 Substituting the value of x back into the expression for y allows finding the value of the second variable.
• ❣️ The solution to the system of equations is represented as an ordered pair (x, y), with x corresponding to the x-value and y corresponding to the y-value.

Questions & Answers

Q: What method does the video use to solve the system of equations?

The video uses the substitution method to solve the system of equations. This involves isolating one variable in one equation and substituting its expression into the other equation.

Q: How is the first equation modified after substituting the expression for y?

After substituting the expression for y, the first equation becomes 4x + (-9x - 3) = 7. Combining like terms simplifies it to -5x - 3 = 7.

Q: How is the value of x determined?

To find the value of x, the equation -5x - 3 = 7 is solved. By adding 3 to both sides, we get -5x = 10. Dividing both sides by -5 yields x = -2.

Q: How is the value of y determined after finding x?

Once x is found, it is substituted back into the expression for y, which is -3x - 1. Plugging in x = -2, we get y = (5 - 1), resulting in y = 5.

Summary & Key Takeaways

• The video demonstrates how to use the substitution method to solve a system of equations.

• The provided equations are solved step-by-step, substituting one variable with an expression from the other equation to simplify the system.

• The solution is found by finding the value of one variable and substituting it back into one of the original equations to solve for the other variable.