Estimate the solution to the system of these linear equations based on the graph. y = − x + 6 y = 3 x − 2

Answer 1

Based on the graph of the two equations, it appears that the two lines intersect at the point (2,4). Therefore, the solution to the system of linear equations is x = 2 and y = 4.

Answer 2

no

Answer 3

I apologize for the mistake in my previous response. Let's reevaluate the solution based on the graph of the two equations y = -x + 6 and y = 3x - 2:

y = -x + 6 is a line with a negative slope that crosses the y-axis at y = 6.
y = 3x - 2 is a line with a positive slope that crosses the y-axis at y = -2.

By analyzing the graph, we can see that the two lines intersect at the point (2, 4).

Therefore, the solution to the system of linear equations y = -x + 6 and y = 3x - 2 is x = 2 and y = 4.

Answer 4

Determine the number of solutions to this system of linear equations: 2 x + y = 6 4 x + 2 y = 8 (1 point)

Answer 5

To determine the number of solutions to the system of linear equations:

2x + y = 6
4x + 2y = 8

We can simplify the second equation by dividing by 2 to make it:

2x + y = 4

Now, we can compare the two equations:

2x + y = 6
2x + y = 4

Since the coefficients of x and y are the same in both equations, but the constants on the right side are different, the two equations represent parallel lines. Parallel lines do not intersect, which means there are no solutions to this system of linear equations.