Final answer:
To find the solution to the given system of equations, we can use the method of substitution. By expressing y in terms of x using the first equation and substituting it into the second equation, we can solve for x. Substituting the obtained x value back into one of the original equations gives us the value of y. The solution to the system of equations is (6, -8).
Step-by-step explanation:
To find the solution to the system of equations y = 1/3x - 10 and 2x + y = 4, we can use the method of substitution. From the first equation, we can express y in terms of x as y = 1/3x - 10. We can then substitute this expression for y in the second equation. So, 2x + (1/3x - 10) = 4. Simplifying this equation will give us the value of x. Once we have x, we can substitute it back into either of the original equations to solve for y.
Let's start by solving for x in the equation 2x + (1/3x - 10) = 4.
- Multiply through by 3 to clear the fraction: 6x + x - 30 = 12
- Combine like terms: 7x - 30 = 12
- Add 30 to both sides: 7x = 42
- Divide both sides by 7: x = 6
Now, we can substitute x = 6 back into the first equation to solve for y: y = 1/3(6) - 10 = -8. Therefore, the solution to the system of equations is (x, y) = (6, -8).