Hey there! Today we are going to explore how two different lines can cross paths to solve a real-world puzzle.
Imagine you have two different clues, and each clue is a straight line on a graph. A system of equations is just a pair of lines that we look at together at the same time!
When we graph both lines, they usually cross each other at one exact point. This crossing point, called the intersection, is the magical coordinates (x, y) that make both equations true at the same time!
Think of it like two friends walking on different paths. The spot where their paths cross is the only place they can meet up and share a high-five!
✏️ Worked example
Find the solution to this system of equations by graphing:
Line 1: y = x + 1
Line 2: y = -x + 5
Graph the first line, y = x + 1. Start at the y-intercept (0, 1) and use the slope of 1 to go up 1 and right 1.
Graph the second line, y = -x + 5. Start at its y-intercept (0, 5) and use the slope of -1 to go down 1 and right 1.
Look at where the two lines cross on your grid.
Identify the coordinates of that crossing point, which is at (2, 3).
Check your work by plugging x = 2 and y = 3 back into both equations to make sure they both work perfectly!
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