Question

Solve each system using elimination.
8x 2y=20 -4x y=2

Answer 1

To solve the system of equations using elimination, you multiply one of the equations by a constant to eliminate a variable, then add or subtract the equations to eliminate the same variable. Finally, solve for the remaining variable. In this case, multiplying the second equation by 2 and adding the equations gives x = 6. Substituting this value back into one of the equations gives y = 14.

Step-by-step explanation:

To solve the system of equations using elimination:

1. Multiply both sides of the second equation by 2 to eliminate the variable y. This gives you -8x - 2y = 4.
2. Add the two equations together to eliminate the variable y. This gives you 8x - 4x = 20 + 4.
3. Simplify the equation to solve for x. This gives you 4x = 24.
4. Divide both sides of the equation by 4 to solve for x. This gives you x = 6.
5. Substitute the value of x back into one of the original equations to solve for y. Using the first equation: 8(6) - 2y = 20. Simplify and solve for y. This gives you 48 - 2y = 20. Rearrange the equation to isolate y: -2y = 20 - 48. Simplify and solve for y: -2y = -28. Divide both sides of the equation by -2 to solve for y. This gives you y = 14.