solve -15x-2y=-31 4x+6y= 11 using linear combination method?
-15x-2y = -31
4x + 6y = 11
-45x -6y = -93
Add the last two
-41x - -82
x = 2
8 + 6y = 11
6y = 3
y = 1/2
To solve the system of equations using the linear combination method, we need to eliminate one variable by multiplying one or both equations by constants so that the coefficients of one variable will be the same, but with opposite signs when the equations are added or subtracted.
Step 1: Multiply the equations by appropriate constants to make the coefficients of either 'x' or 'y' the same.
First, let's make the coefficients of 'y' the same:
Multiply the first equation by 3 and the second equation by -2:
Equation 1: -45x - 6y = -93 (3 * (-15x - 2y = -31))
Equation 2: -8x - 12y = -22 (-2 * (4x + 6y = 11))
Step 2: Add the two new equations together to eliminate the variable 'y'.
Add Equation 1 + Equation 2:
-45x - 6y + (-8x) - 12y = -93 + (-22)
This simplifies to:
-53x - 18y = -115
Step 3: Solve the resulting equation for 'x'.
Next, we can solve the equation -53x - 18y = -115 for 'x'.
-53x - 18y = -115
Step 4: Solve for 'y'.
Now that we have the value of 'x', we can substitute it back into one of the original equations to solve for 'y'.
Let's substitute the value of 'x' into the first equation:
-15x - 2y = -31
-15 * (-2) - 2y = -31
30 - 2y = -31
Step 5: Solve for 'y'.
Solve the above equation for 'y':
-2y = -31 - 30
-2y = -61
Dividing by -2:
y = 61 / 2
So the value of 'y' is 30.5.
Step 6: Write the solution.
The solution to the system of equations is 'x = -2' and 'y = 30.5'.
Therefore, the solution to the system of equations -15x - 2y = -31 and 4x + 6y = 11 using the linear combination method is 'x = -2' and 'y = 30.5'.