Question

Solve using the elimination metr 6x-y=39 7x+y=52

Answer 1

The solution to the system of equations 6x-y=39 and 7x+y=52 using the elimination method is x = 7 and y = 3. This is found by adding the two equations to eliminate y, which gives us a solvable equation for x, and then substituting the value of x back into one of the original equations to solve for y.

Step-by-step explanation:

To solve the system of equations 6x-y=39 and 7x+y=52 using the elimination method, we need to eliminate one of the variables. We can do this by adding the two equations together because the y variables will cancel out as they have opposite coefficients.

1. Add the two equations: (6x - y) + (7x + y) = 39 + 52.
2. Simplify the left side by combining like terms: 6x + 7x = 13x and -y + y = 0, which eliminates y.
3. Simplify the right side by adding the constants: 39 + 52 = 91.
4. Now we have a simple equation, 13x = 91.
5. Divide both sides by 13 to solve for x: x = 91 / 13.
6. Calculate the value of x: x = 7.
7. Now substitute x back into one of the original equations to find y. Let's use the first equation, 6x - y = 39.
8. Substitute x: 6(7) - y = 39.
9. Multiply 6 times 7: 42 - y = 39.
10. Subtract 42 from both sides: -y = -3.
11. Multiply both sides by -1 to get y: y = 3.

Therefore, the solution to the system is x = 7 and y = 3.