Question 4: One Solution
Consider the two equations you underlined, which form a system with one solution.
Graph them together on the following coordinate grid.
What do you notice about these equations? What does it mean for a system to have
one solution? Explain what it means graphically for a system to have one solution.
Equation 1: y = 2x + 1
Equation 2: y = -3x + 5
To graph these equations, we can plot a few points and then draw a line passing through them for each equation. For the first equation, we can plot the points (0,1) and (1,3) to draw a line passing through them. For the second equation, we can plot the points (0,5) and (1,2) to draw a line passing through them.
When we graph these two equations on the coordinate grid, we notice that the two lines intersect at a single point, which is the solution to the system of equations. This means that there is only one combination of x and y values that satisfy both equations simultaneously.
Graphically, having one solution means that the two lines representing the equations intersect at a single point. This point is the solution to the system of equations, where the x and y values satisfy both equations at the same time. This unique point of intersection signifies that there is only one solution to the system of equations.