Question

Here is a system of equations. {y= 2x+5 {y= x+1 Graph the system. Then write its solution. Note that you can also answer “ No solution” or “infinitely many” solutions.

Answer 1

Solution: (-4, -3)

Step-by-step explanation

The solution of a system of linear equations is the point where the graphs of the equations intersect. If the lines are parallel, there is no solution - parallel lines do not intersect, and if the equations represent the same line, there are infinitely many solutions.

In this case, we have the equations y = 2x + 5 and y = x+1. The graphs are:

The green line is the graph of y = 2x + 5. The red line is the graph of the equation y = x + 1.

As we can see, the lines intersect at the point (-4, -3). This is the solution.