Final answer:
To solve the system of equations using elimination, multiply one or both equations by a number to make the coefficients of one of the variables equal. Then, add the equations together to eliminate one variable and solve for the remaining variable. Finally, substitute the value of the variable into one of the original equations to solve for the other variable and check the solution. The solution to the system of equations is x = 5 and y = -2.
Step-by-step explanation:
To solve the system of equations using elimination:
- Multiply one or both equations by a number to make the coefficients of one of the variables equal.
- Add the equations together to eliminate one variable.
- Solve for the remaining variable.
- Substitute the value of the variable into one of the original equations to solve for the other variable.
- Check the solution by substituting the values into both equations and ensuring they are true.
For the given system of equations, let's start by multiplying the second equation by -1 to eliminate the x variable. The new system is: 6x + 10y = 10 and 6x + 24y = -18. Subtract the second equation from the first equation to eliminate the x variable. This gives us: 6x + 10y - (6x + 24y) = 10 - (-18), which simplifies to -14y = 28.
Divide both sides of the equation by -14 to solve for y: y = -2.
Now substitute the value of y back into one of the original equations. Using the first equation: 6x + 10(-2) = 10. Simplifying this, we get 6x - 20 = 10. Add 20 to both sides: 6x = 30. Divide both sides by 6: x = 5.
The solution to the system of equations is x = 5 and y = -2.