Use the table to answer the question

Question

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x-value | y-value if y= 2x – 5 | y-value if y= x – 3
0 | -5 | -3
1 | -3 | -2
2 | -1 | -1
3 | 1 | 0
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Jain made a table showing some x- and y-values in a system of equations. Use his table to identify the solution for the system.

A. (3,0)
B. (2,-1)
C. There is an infinite number of solutions
D. There is no solution

Answer 1

To find the solution for the system of equations using Jain's table, we need to identify the point where the two equations intersect, which means their y-values are equal for the same x-value.

From the table, we can see the y-values for both equations:

For the equation \( y = 2x - 5 \):

• When \( x = 0 \), \( y = -5 \)
• When \( x = 1 \), \( y = -3 \)
• When \( x = 2 \), \( y = -1 \)
• When \( x = 3 \), \( y = 1 \)

For the equation \( y = x - 3 \):

• When \( x = 0 \), \( y = -3 \)
• When \( x = 1 \), \( y = -2 \)
• When \( x = 2 \), \( y = -1 \)
• When \( x = 3 \), \( y = 0 \)

Now let's compare the y-values for the same x-values:

• For \( x = 0 \): \( y = -5 \) (from \( y = 2x - 5 \)) and \( y = -3 \) (from \( y = x - 3 \)) → not equal
• For \( x = 1 \): \( y = -3 \) and \( y = -2 \) → not equal
• For \( x = 2 \): \( y = -1 \) and \( y = -1 \) → equal
• For \( x = 3 \): \( y = 1 \) and \( y = 0 \) → not equal

The only point where both equations yield the same y-value is at \( x = 2 \) with \( y = -1 \).

Thus, the solution to the system of equations is \( (2, -1) \).

The answer is B. (2, -1).