Determine whether each ordered pair is a solution of the...

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}4 x=1-y \\ x-3 y=-8\end{array}\right.$
a. (0,1)
b. $\left(\frac{1}{6}, \frac{1}{3}\right)$

Key Concepts

Ordered Pair as a Solution

An ordered pair represents a potential solution to a system of equations, where the first number corresponds to the value of the first variable and the second number corresponds to the value of the second variable. To be a valid solution, the pair must satisfy each equation in the system.

Substitution/Verification Method

The substitution or verification method involves plugging the values of the ordered pair into each equation to determine if the equations hold true. This process is essential for confirming whether a given pair of numbers is indeed a solution to the system.

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The solution is any set of values that satisfies all equations simultaneously. This concept is fundamental in algebra and is used to find the point(s) of intersection between the lines described by the equations.

Transcript

00:01 Number eight, we're just testing points to see if they are solution to a system of linear equations.

00:07 And i'm going to plug in my variables and see if it gives me true statements for both equations.

00:12 Now, the first point for part a is pretty simple, but part b is a little more complicated because it has fractions.

00:18 So we're going to work through that.

00:20 So for the first one, i'm going to go ahead and plug in zero for my x value and one for my y value.

00:26 I'm going to start with the first equation.

00:27 So 4 times 0 equals 1 minus 1.

00:35 So 4 times 0 is 0.

00:37 1 minus 1 is 0.

00:39 So therefore it is good for the first equation.

00:42 So i'm going to check my second equation.

00:47 So x is 0 again.

00:49 So 0 minus 3 times 1 is that equal to negative 8.

00:55 Negative 3 times 1 is negative 3, which is not equal to negative 8.

01:00 So therefore, the first point, 01, is not a solution to the system of linear equations, which means it's not the intersection point to those two lines.

01:20 All right, part b, a lot more difficult because it's fractions.

01:25 It takes a little bit of work.

01:29 My x value is one -sixth.

01:31 My y value is one -third.

01:33 Now, if you have a nice calculator, you can just put in the equation and see if it's true.

01:40 But i'm going to do the algebra so that we can see how that works.

01:45 So for the first equation, i have 4x equals 1 minus y.

01:49 So i'm going to have 4 times 1 6th.

01:53 And i'm going to put 4 over 1 so that i can multiply that out equals 1 minus 1 3rd.

02:05 All right.

02:06 So i'm going to simplify before i even multiply these fractions on the left.

02:12 So both 4 and 6 are even.

02:14 So i can divide them by two and this becomes a two and this becomes a three...

Please give Ace some feedback