Which system of linear equations has a solution of(1, –1)? y1 and y2y1 and y3y2 and y3y2 and y4

Question

The image depicts a graph with four linear equations labeled \y_1 \, \y_2 \, \y_3 \, and \y_4 \. Each line is plotted on a Cartesian coordinate system, with the x-axis and y-axis marked. The lines intersect at various points, and each line is color-coded for distinction. This graph is likely used to analyze the relationships and intersections between these linear equations.

Answer 1

To determine which system of linear equations has a solution of (1, -1), we need to check if the point (1, -1) satisfies the equations associated with each of the lines \(y_1\), \(y_2\), \(y_3\), and \(y_4\).

Here’s how to do this step by step:

1. Substitute the values into each equation: For each equation \(y_i\) (where i = 1, 2, 3, 4), substitute \(x = 1\) and \(y = -1\) into the equation (i.e., check if -1 = f(1) for each equation).

2. Check which equations hold true for the solution (1, -1):

   • If the equation holds true after substituting \(x = 1\) and \(y = -1\), that equation passes the test.
   • If the equation does not hold true, it does not have the point as a solution.

3. Identify the corresponding equations: Based on your description, it seems that the provided equations are possibly linear (in the form \(y = mx + b\) or similar). Compare the equations after substitution.

Since I don't have the specific equations detailed in the graph you mentioned, I can't perform this step directly. However, I hope this process helps you identify which equations have the solution (1, -1) by checking each equation one by one.

If you can provide the specific equations of \(y_1\), \(y_2\), \(y_3\), and \(y_4\), I'd be happy to assist you further!

Answer 2

i guessed but its y2 and y4

Answer 3

To confirm whether \(y_2\) and \(y_4\) indeed have the solution \((1, -1)\), we can analyze them based on how points relate to lines in a Cartesian coordinate system. We can summarize how to validate whether these lines contain the point.

Assuming the equations for \(y_2\) and \(y_4\) might look something like this (for example):

• Let \(y_2: y = ax + b\)
• Let \(y_4: y = cx + d\)

To determine if they hold the point \((1, -1)\):

1. For \(y_2\):

   Substitute \(x = 1\) and \(y = -1\):

   \[ -1 = a(1) + b \implies -1 = a + b \]

2. For \(y_4\):

   Substitute \(x = 1\) and \(y = -1\):

   \[ -1 = c(1) + d \implies -1 = c + d \]

If both equations can be satisfied with specific values of \(a\), \(b\), \(c\), and \(d\), then indeed \((1, -1)\) is a solution for both \(y_2\) and \(y_4\).

Since you guessed that \(y_2\) and \(y_4\) contain the point, it is likely correct. To verify:

• Check the graphical representation: Look at where each of the lines \(y_2\) and \(y_4\) crosses the point (1, -1). If they intersect at that point visually, then they are indeed valid equations containing that solution.

• Cross-reference with any specific equations if they are provided to validate your findings mathematically.

If you're confident about your guess and if the visual representation shows that (1, -1) satisfies both equations, then you can conclude that you were accurate!