Question

Solve the linear equations by elimination.

A. x = 5, y = 3
B. x = 3, y = 5
C. x = 4, y = 2
D. x = 2, y = 4

Answer 1

To solve the given linear equations by elimination, we need to convert the coefficients of one variable into opposites and eliminate that variable. After performing the necessary operations, the solution to the given equations is x = -503/78 and y = -57/13.

Step-by-step explanation:

To solve the given linear equations by elimination, we can eliminate one of the variables by multiplying one or both of the equations by a suitable constant so that the coefficients of one variable become opposites.

Let's solve the simultaneous equations:

1. 7y = 6x + 8
2. 4y = 8
3. y + 7 = 3x

To eliminate the variable y, we can multiply the second equation by 7:

1. 7y = 6x + 8
2. 28y = 56
3. y + 7 = 3x

Now we can eliminate y from the first and third equations:

1. 28y = 56
2. 7y = 6x + 8
3. y + 7 = 3x

By subtracting the second equation from the first equation, we can solve for x:

• (-7y) = (6x + 8) - 28y
• -7y = 6x - 28y + 8
• -21y = 6x + 8
• 6x + 21y = -8

By substituting the value of x in terms of y into the third equation, we can solve for y:

• y + 7 = 3x
• y + 7 = 3(-2y/7) - 8/7
• y + 7 = -6y/7 - 8/7
• 7(y + 7) = -6y - 8
• 7y + 49 = -6y - 8
• 13y = -57
• y = -57/13

Finally, we can substitute the obtained value of y into the first equation to solve for x:

• 7y = 6x + 8
• 7(-57/13) = 6x + 8
• -399/13 = 6x + 8
• 6x = -399/13 - 104/13
• 6x = -503/13
• x = -503/78

Therefore, the solution to the given linear equations by elimination is x = -503/78 and y = -57/13.