solve by elimination x+6y=12
-x+7y=1
x + 6y = 12 --- Equation 1
-x + 7y = 1 --- Equation 2
13y = 13
y = 13/13
y = 1
sub y = 1 in equation 1 we get:
x + 6y = 12
x + 6(1)= 12
x + 6 = 12
x = 12 - 6
x = 6
Hence, x = 6 when y = 1
To solve this system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations. Let's go step by step:
1. Multiply the first equation by -1 to make the x-term negative:
-1 * (x + 6y) = -1 * 12
-x - 6y = -12
2. Write down the new equation along with the second equation:
-x - 6y = -12
-x + 7y = 1
3. Now, add the two equations together to eliminate the x-term:
(-x - 6y) + (-x + 7y) = -12 + 1
-2x + y = -11
4. Now we have a new equation: -2x + y = -11
To solve for the remaining variable, we can use the other equation:
5. Multiply the second equation by 2 to make its coefficient of the x-term match the coefficient in the third equation:
2 * (-x + 7y) = 2 * 1
-2x + 14y = 2
6. Write down the new equation along with the third equation:
-2x + 14y = 2
-2x + y = -11
7. Subtract the two equations to eliminate the y-term:
(-2x + 14y) - (-2x + y) = 2 - (-11)
13y = 13
8. Now we have a new equation: 13y = 13
To solve for y, divide both sides of the equation by 13:
13y / 13 = 13 / 13
y = 1
9. Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
x + 6y = 12
x + 6(1) = 12
x + 6 = 12
x = 12 - 6
x = 6
So the solution to the system of equations is x = 6 and y = 1.