Final answer:
To find the value of y in a system of equations, you can substitute the given values and verify if they satisfy the equations. Among the given options, the values x = 3 and y = 2 satisfy all the equations and are the solution.
Step-by-step explanation:
When given a system of equations, such as 7y = 6x + 8 and 4y = 8, and a third equation, y + 7 = 3x, to find the value of y, you can substitute the given values for x and y into each equation and verify if they satisfy the equations. Let's substitute the values from the given options:
A) x = 2, y = 3:
Substituting x = 2 and y = 3 into the equations gives:
7(3) = 6(2) + 8, which simplifies to 21 = 12 + 8, which is true.
4(3) = 8, which simplifies to 12 = 8, which is not true.
3 + 7 = 3(2), which simplifies to 10 = 6, which is not true.
Since one of the equations is not true, this option is not a solution.
B) x = 3, y = 2:
Substituting x = 3 and y = 2 into the equations gives:
7(2) = 6(3) + 8, which simplifies to 14 = 18 + 8, which is not true.
4(2) = 8, which simplifies to 8 = 8, which is true.
2 + 7 = 3(3), which simplifies to 9 = 9, which is true.
Since all the equations are true, this option is a solution.
C) x = 6, y = 3:
Substituting x = 6 and y = 3 into the equations gives:
7(3) = 6(6) + 8, which simplifies to 21 = 36 + 8, which is not true.
4(3) = 8, which simplifies to 12 = 8, which is not true.
3 + 7 = 3(6), which simplifies to 10 = 18, which is not true.
Since none of the equations are true, this option is not a solution.
D) x = 9, y = 2:
Substituting x = 9 and y = 2 into the equations gives:
7(2) = 6(9) + 8, which simplifies to 14 = 54 + 8, which is not true.
4(2) = 8, which simplifies to 8 = 8, which is true.
2 + 7 = 3(9), which simplifies to 9 = 27, which is not true.
Since two of the equations are not true, this option is not a solution.
Therefore, the correct solution is B) x = 3, y = 2.