Determine the solution to each system of equations by...

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Key Concepts

Substitution Method

The substitution method is a technique for solving systems of equations in which one equation is manipulated to express one variable in terms of the other(s). This expression is then substituted into the other equation(s), effectively reducing the number of variables and allowing for a step-by-step solution.

Manipulating Fractional Coefficients

When equations include fractional coefficients, it is often helpful to clear the fractions by multiplying both sides of the equation by the least common denominator. This simplification makes the arithmetic more straightforward and reduces the risk of errors during the solving process.

Systems of Linear Equations

Systems of linear equations involve multiple equations with several variables that are solved simultaneously. Each equation represents a linear relationship, and finding the solution means identifying the common values of the variables that satisfy all equations in the system.

Transcript

00:01 Okay, we're going to solve this set by the system by substitution, which means we need to get a variable by itself.

00:10 So if i look at this y, it's almost by itself already.

00:14 So i'm just going to swap it with the 9.

00:16 So i'm going to add y, and i'm going to subtract 9.

00:20 So i'm going to have 3x minus 9 equals positive y.

00:27 So now we can substitute the y on the, this top equation here.

00:33 So i'm going to have one fifth x, that doesn't change, plus two thirds, but instead of saying y, i'm going to say 3x minus 9 equals negative 8ths.

00:48 So now let's distribute.

00:50 We have 1 fifth x plus 2x because our 3s are going to cancel out, minus 6 because 2 times 9 is 18, 18 divided by 3 is 6 equals negative 8ths.

01:11 So now, if i want to keep this as fifths, 2 is the same thing.

01:17 I'm going to write it just at the top here.

01:19 2 is the same thing as 10 5ths, right? because 10 divided by 5 is 2.

01:24 So if i combine these, i can say 11 fifths x minus 6 equals negative 8 fifths.

01:35 So now i'm going to pause here, and i'm going to get rid of our 5.

01:40 And the way we can do this is multiplying the entire equation by 5.

01:45 So for here, it's going to cancel out and say 11x...