Solving Systems of Linear Equations Graphically

To graph the equations, first we use their constants to plot the $y$-intercepts. It is the number of people that live in the country $2019,$ when $x=0.$

Now, we will use the information about the slope. In this case it is how much the population increase each year. Since it is hard to plot decimals in the graph, let's rewrite the slopes as rise and run. $$\begin{array}{r}\text{China: }0.01\cdot \frac{10}{10}=\frac{0.1}{10}\\ \text{India: }0.03\cdot \frac{10}{10}=\frac{0.3}{10}\end{array}$$ Thus, for $10$ step to the right on the $x$-axis, we should move $0.1$ and $0.3$ units up.

The graphs can now be completed with lines through the points.

To find the year where the populations will be equal, we have to determine the point at which the graphs intersect.

When $x=10$ the countries will have the same population. Since $x$ is described as years after 2019 we should add $10$ to $2019$ to find the correct year. $$2019+10=2029$$