Question

What is the solution to this system of linear equations? 8x + 2y = 2 and x + 3y = 14

Answer 1

The solution to the system of linear equations 8x + 2y = 2 and x + 3y = 14 is x = -1 and y = 5.

Step-by-step explanation:

To find the solution to the system of linear equations 8x + 2y = 2 and x + 3y = 14, we can use the method of substitution or elimination. Let's use the substitution method:

1. From the second equation, solve for x: x = 14 - 3y
2. Substitute this value of x into the first equation: 8(14 - 3y) + 2y = 2
3. Simplify and solve for y: 112 - 24y + 2y = 2. Combine like terms: -22y = -110. Divide both sides by -22: y = 5
4. Substitute the value of y back into the second equation to solve for x: x + 3(5) = 14. Simplify: x + 15 = 14. Subtract 15 from both sides: x = -1

So, the solution to the system of linear equations is x = -1 and y = 5.