Question

What is the solution to the system of equations 8x − 2y = 0 and -6x + 14y = 50?

a) x = 4, y = 16
b) x = -2, y = 10
c) x = 6, y = 25
d) x = -4, y = -14

Answer 1

The solution to the system of equations 8x - 2y = 0 and -6x + 14y = 50 is x = 1, y = 4. This solution is found using the elimination method. None of the given options correctly matches this solution.

Step-by-step explanation:

The solution to the system of equations 8x − 2y = 0 and −6x + 14y = 50 can be found by using either the substitution method or the elimination method. To solve these linear equations, we will use the elimination method by multiplying the first equation by 3 and the second equation by 2 to eliminate x when we add them together:

• 24x − 6y = 0 (equation 1 multiplied by 3)
• −12x + 28y = 100 (equation 2 multiplied by 2)

Add the two equations:

• (24x + −12x) + (−6y + 28y) = 0 + 100
• 12x + 22y = 100

Divide every term by 2:

• 6x + 11y = 50

Now we solve for y using the first equation:

• 8x = 2y
• y = 4x

Substitute y = 4x into 6x + 11y = 50:

• 6x + 11(4x) = 50
• 6x + 44x = 50
• 50x = 50
• x = 1

Substitute x = 1 into y = 4x:

• y = 4(1)
• y = 4

The solution to the system of equations is x = 1, y = 4. None of the given options a) x = 4, y = 16 b) x = -2, y = 10 c) x = 6, y = 25 d) x = -4, y = -14 is correct. The correct answer is not provided in the given options.