Solution Sets of Simultaneous Equations Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items

Question
Use the table to answer the question.

x-value y-value if y=x+6
y-value if y=2x+3
0 6 3
1 7 5
2 8 7
3 9 9
4 10 11
A system of equations is displayed in the table. What is the solution for the system?

(1 point)
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Answer 1

To find the solution for the system of equations given in the table, we need to identify the x-value where the two equations \( y = x + 6 \) and \( y = 2x + 3 \) have the same y-value.

Let's look at the y-values from both equations in the table:

• For \( x = 0 \):

  • \( y = x + 6 = 0 + 6 = 6 \)
  • \( y = 2x + 3 = 2(0) + 3 = 3 \)

• For \( x = 1 \):

  • \( y = x + 6 = 1 + 6 = 7 \)
  • \( y = 2x + 3 = 2(1) + 3 = 5 \)

• For \( x = 2 \):

  • \( y = x + 6 = 2 + 6 = 8 \)
  • \( y = 2x + 3 = 2(2) + 3 = 7 \)

• For \( x = 3 \):

  • \( y = x + 6 = 3 + 6 = 9 \)
  • \( y = 2x + 3 = 2(3) + 3 = 9 \)

• For \( x = 4 \):

  • \( y = x + 6 = 4 + 6 = 10 \)
  • \( y = 2x + 3 = 2(4) + 3 = 11 \)

The two equations yield the same y-value at \( x = 3 \), where both equations give \( y = 9 \).

Therefore, the solution to the system of equations is:

\[ (3, 9) \]