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Hey there! Today we are going to explore how two different mathematical clues can work together to help us find one perfect, hidden answer.
Imagine you are trying to guess two secret numbers. If I only tell you that they add up to 10, there are too many possibilities! It could be 5 and 5, 8 and 2, or even 9 and 1.
But what if I give you a second clue? If I also tell you that one number is 4 bigger than the other, suddenly there is only one correct answer: 7 and 3! In math, having two or more equations working together is called a system of equations.
We can think of these equations as two lines on a graph. The first equation makes one line, and the second equation makes another. The magic spot where they cross over each other is the single solution that solves both equations at the same time!
Solve the system of equations by graphing: 1) y = x + 1 2) y = -x + 5
- Graph the first line, y = x + 1. It starts on the y-axis at 1, and goes up 1 unit for every 1 unit it moves to the right.
- Graph the second line, y = -x + 5. It starts on the y-axis at 5, and goes down 1 unit for every 1 unit it moves to the right.
- Look at the grid to find where the two lines cross.
- Identify the coordinates of that crossing point. The lines intersect perfectly at the point (2, 3).
- Check your work! Plug x = 2 and y = 3 back into both equations. Since 3 = 2 + 1 and 3 = -2 + 5 are both true, (2, 3) is our correct solution!
