Use the table showing state populations. 1 California 25,484,000 567,000 2

step 1 Hello, today we are looking at systems of equations and their inequalities. So in this problem,

Use the table showing state populations. 1 ...

Use the table showing state populations. $\begin{array}{|c|c|c|c|c|}\hline 1 & {\text { California }} & {25,484,000} & {567,000} \\ \hline 2 & {\text { Texas }} & {22,118,000} & {447,000} \\ \hline 3 & {\text { New York }} & {19,190,000} & {70,000} \\ \hline 4 & {\text { Florida }} & {17,019,000} & {304,000} \\ \hline 5 & {\text { lllinois }} & {12,653,000} & {80,000} \\ \hline\end{array}$ Graph both equations for the years 2003 to 2020. Estimate when the populations of both states will be equal.

Use the table showing state populations.
$\begin{array}{|c|c|c|c|c|}\hline 1 & {\text { California }} & {25,484,000} & {567,000} \\ \hline 2 & {\text { Texas }} & {22,118,000} & {447,000} \\ \hline 3 & {\text { New York }} & {19,190,000} & {70,000} \\ \hline 4 & {\text { Florida }} & {17,019,000} & {304,000} \\ \hline 5 & {\text { lllinois }} & {12,653,000} & {80,000} \\ \hline\end{array}$
Graph both equations for the years 2003 to 2020. Estimate when the populations of both states will be equal.

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Key Concepts

Systems of Linear Equations

Systems of linear equations consist of two or more linear functions that are solved simultaneously. In practical scenarios like population comparisons, solving such systems allows us to determine when two different linear trends converge, providing insights into future scenarios based on current data.

Linear Functions

Linear functions describe relationships where a constant rate of change exists. In the context of population projections, these functions model how a quantity changes over time under steady growth assumptions. They are defined by a slope and an intercept, making them straightforward to graph and analyze over specified time intervals.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy a given linear function and drawing the line that represents all solutions. This visual representation helps in understanding trends over time, comparing different data sets, and identifying key features like intercepts and slopes.

Intersection Points

The intersection point of two linear functions is where the values of the functions are equal, representing the solution to the system of equations formed by these lines. In population modeling, finding the intersection point can indicate the time at which two growing populations become equal.

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