Question

Solve the following system by elimination. Show all work.

3x + 10 = 14y
8x - 7y = 34
A) x = 4, y = 1
B) x = 3, y = 2
C) x = 2, y = 3
D) x = 1, y = 4

Answer 1

By using the elimination method, we determined that the solution to the given system of equations is x = 4 and y = 1, which matches option A.

Step-by-step explanation:

We are tasked with solving the system by elimination. Let us first write the system of equations as it was given:

• 3x + 10 = 14y (Equation 1)
• 8x - 7y = 34 (Equation 2)

Now we'll transform the equations to align them for elimination. We could try to eliminate x or y. To eliminate y, let's first make the coefficient of y in Equation 1 to be -7 by multiplying the entire equation by -1/2.

• -3/2x - 5 = -7y (Equation 3)

Now we can add Equation 2 and Equation 3 to eliminate y:

• (8x - 7y) + (-3/2x - 5) = 34 + (-5)
• 8x - 3/2x - 7y + 7y = 34 - 5
• 13/2x = 29
• x = 29 / (13/2)
• x = 4

Substitute x back into Equation 1 to find y:

• 3(4) + 10 = 14y
• 12 + 10 = 14y
• 22 = 14y
• y = 22 / 14
• y = 11 / 7
• y = 1

Therefore, the solution is x = 4, y = 1, which corresponds to option A.