Solve a system of equations by graphing: word problems

Learning Objectives Identify unknown quantities and define variables in word problems. Translate real-world scenarios into two linear equations. Graph pairs of linear equations accurately on a coordinate plane. Determine the solution to a system of equations by finding the intersection point of their graphs. Interpret the coordinates of the intersection point as the solution to the original word problem. Verify the solution by substituting values back into the original equations or problem context. Ever wonder how stores figure out when two different sales promotions will cost the same? 🤔 Or how two friends walking at different speeds will meet? In this lesson, you'll learn how to solve real-world puzzles by turning them into math equations and then drawing pictures (...

TermDefinitionExample System of EquationsTwo or more equations that share the same variables and whose solutions must satisfy all equations simultaneously.The equations `y = 2x + 1` and `y = -x + 4` form a system of equations. Linear EquationAn equation whose graph is a straight line. It usually has variables raised to the power of 1.`y = 3x - 2` or `x + y = 5` are linear equations. VariableA symbol, usually a letter, that represents an unknown number or quantity in an equation.In the problem 'Sarah has 5 more apples than John', we might use `x` for John's apples and `y` for Sarah's apples. Graphing an EquationThe process of drawing the line that represents all the possible solutions to a linear equation on a coordinate plane.Plotting points like (0, -2), (1, 1), (2, 4...

Slope-Intercept Form $y = mx + b$ This form is ideal for graphing. '$m$' represents the slope (how steep the line is, rise over run), and '$b$' represents the y-intercept (where the line crosses the y-axis). Graphing a Linear Equation 1. Plot the y-intercept ($b$) on the y-axis. 2. Use the slope ($m = \frac{\text{rise}}{\text{run}}$) to find a second point. 3. Draw a straight line through the two points. This rule guides you on how to visually represent an equation on a coordinate plane. Remember positive slope goes up-right, negative slope goes down-right. Solving a System by Graphing 1. Graph both linear equations on the same coordinate plane. 2. Identify the coordinates $(x, y)$ of the point where the two lines intersect. This point is the soluti...