Solve one of these systems of equations by drawing a graph....

Solve one of these systems of equations by drawing a graph. Solve the other by substitution.
$$
\begin{array}{cc}{\mathbf{a} \cdot f+g=20} & {\text { b. } y-x=3} \\ {3 f+g=28} & {2 y+3 x=16}\end{array}
$$

Key Concepts

Substitution Method for Solving Systems

The substitution method involves isolating one variable in one equation, then substituting that expression into the other equation. This process reduces the system to a single equation with one variable, which can then be solved, and the result substituted back to find the value of the other variable.

System of Linear Equations

A system of linear equations consists of two or more equations with the same set of variables and is solved by finding the variable values that satisfy all equations simultaneously. This concept is fundamental in algebra and is used to model situations where multiple conditions must be met.

Graphical Method for Solving Systems

The graphical method involves plotting each equation on a coordinate plane and finding the point where the graphs intersect. This intersection represents the solution to the system, as it is the set of variable values that satisfies all equations simultaneously.

Transcript

00:02 This problem gives us two system of equations.

00:07 I'm going to solve the first system, system a, using the graphing method.

00:13 I'm going to first start by making a table so i can figure out what my coordinates are going to be.

00:22 So i'm simply going to write a column for f and then put my equation in the middle.

00:28 I'm going to look at f plus g equals 21st and then my output, which will be g.

00:36 Now i want to choose relatively small numbers, and you might have to kind of guess and check what numbers you use.

00:43 I'm going to go ahead and use two, three, and four.

00:51 Okay, let's go ahead and plug those in.

00:53 So i have two plus g equals 20, so that will come out to be 18.

01:01 3 plus g equals 20, so that will be 17, and 4 plus g equals 20, so that will be 16.

01:15 Now let's move on to the next equation.

01:18 Again, i'm going to draw the exact same table here, using the second equation, 3f plus g equals 28, and i'm going to use the same values, 2, 3, and 4.

01:39 So let's start to plug these in.

01:41 I have 3 times 2 plus g equals 28.

01:48 So now i need to think in my head, 3 times 2 is 6, and then i'll be doing 28 minus 6, which is 22.

02:01 Next one, i have 3 times 3 plus g equals 28.

02:08 3 times 3 is 9, and then 28.

02:12 Minus 9 is 19.

02:17 Next one, 3 times 4 plus g equals 28.

02:24 3 times 4 is 12.

02:28 So 28 minus 12 is 16.

02:32 And you can see in the charts, just by looking at them, i have the same input and output right here...