using elimination method
x + 6y = 58
-x + 7y = 59
Help please!!!!
http://www.mathplanet.com/education/algebra-1/systems-of-linear-equations-and-inequalities/the-elimination-method-for-solving-linear-systems
x + 6y = 58
-x + 7y = 59
13y = 117
y = 9
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations (if necessary) by a constant to get the coefficients of one of the variables to be the same.
In this case, you can multiply the first equation by -1 to make the coefficients of "x" opposites:
-(x + 6y) = -58
-x - 6y = -58
Step 2: Add the two equations together to eliminate one variable.
Now, add the two equations:
(-x - 6y) + (-x + 7y) = -58 + 59
Simplifying the equation, we get:
-2x + y = 1
Step 3: Solve the resulting equation for one variable.
Rearrange the equation to solve for "y":
y = 1 + 2x
Step 4: Substitute the value of the variable found in step 3 into one of the original equations to find the value of the remaining variable.
Substitute "y = 1 + 2x" into the first equation:
x + 6(1 + 2x) = 58
Simplify the equation:
x + 6 + 12x = 58
13x + 6 = 58
13x = 52
x = 4
Step 5: Substitute the value of x into one of the original equations to find the value of y.
Substitute x = 4 into the second equation:
-x + 7y = 59
-4 + 7y = 59
7y = 59 + 4
7y = 63
y = 9
Therefore, the solution to the system of equations is x = 4 and y = 9.