Final answer:
To solve the system of equations 2x - 6y = 8 and 6x + 10y = -4, you can use the method of elimination. Multiply the equations to eliminate the x term, add the equations to find the y value, and substitute the y value to solve for x.
Step-by-step explanation:
To solve the system of equations:
2x - 6y = 8
6x + 10y = -4
You can use the method of elimination or substitution. Here, I will show you the method of elimination:
- First, multiply the first equation by 3 and the second equation by -1 to eliminate the x term.
- The new system of equations is: 6x - 18y = 24 and -6x - 10y = 4.
- Add the two equations together: -28y = 28.
- Divide both sides by -28 to solve for y: y = -1.
- Substitute the value of y into one of the original equations (let's use the first one): 2x - 6(-1) = 8.
- Simplify the equation: 2x + 6 = 8.
- Subtract 6 from both sides: 2x = 2.
- Divide both sides by 2 to solve for x: x = 1.
Therefore, the solution to the system of equations is x = 1 and y = -1.