When they say "Find the solution to this system" they mean where the lines intercept correct?
Probably.
yes.
Yes, when someone says "find the solution to this system," they are typically referring to finding the point where the lines in the system intersect. In a system of linear equations, each equation represents a line on a coordinate plane. The solution to the system is the point at which these lines intersect, if they do.
To find the solution to a system of linear equations, you have a few methods:
1. Graphing: You can graph each equation on the coordinate plane and visually find the point where the lines intersect. This point represents the solution to the system.
2. Substitution: In this method, you solve one of the equations for one variable and substitute this expression into the other equation. By solving for the remaining variable, you find its value. Substituting this value back into either of the original equations gives you the value of the second variable. The resulting values form the solution to the system.
3. Elimination: This method involves manipulating the equations to eliminate one variable by adding or subtracting the equations. By eliminating one variable, you can solve for the other variable, which allows you to determine its value. Substituting this value back into either of the original equations will give you the value of the second variable. The resulting values make up the solution to the system.
The goal of any of these methods is to find the point of intersection of the lines, which represents the solution to the system of linear equations.