# Solving a System of Equations by Substitution | Summary and Q&A

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September 15, 2016
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blackpenredpen
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.

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### 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.