solving systems of equations by graphing pratice

Answer 1

1. Solve the system of equations by graphing:
y = 2x + 1
y = -3x + 5

To graph these equations, we first need to determine two points for each equation. For the first equation, y = 2x + 1, we can choose x = 0 and x = 1:
When x = 0, y = 2(0) + 1 = 1
When x = 1, y = 2(1) + 1 = 3

For the second equation, y = -3x + 5, we can choose x = 0 and x = 1:
When x = 0, y = -3(0) + 5 = 5
When x = 1, y = -3(1) + 5 = 2

Now, plot these points on a graph and draw a line through them. The two lines will intersect at the point (2,5), which is the solution to the system of equations.

2. Solve the system of equations by graphing:
y = x + 2
y = -x + 4

Again, we need to determine two points for each equation. For the first equation, y = x + 2, we can choose x = 0 and x = 1:
When x = 0, y = 0 + 2 = 2
When x = 1, y = 1 + 2 = 3

For the second equation, y = -x + 4, we can choose x = 0 and x = 1:
When x = 0, y = -0 + 4 = 4
When x = 1, y = -1 + 4 = 3

Plot these points on a graph and draw a line through them. The two lines will intersect at the point (2,4), which is the solution to the system of equations.