Question

Solve each system by elimination. 3m + 4n = -13 , 5m + 6n = -19

Answer 1

To solve the system of equations by elimination, we multiply the equations to eliminate a variable, subtract the equations to solve for the other variable, and substitute the value back to find the solution.

Step-by-step explanation:

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable m by multiplying the first equation by 5 and the second equation by 3. This will give us:

15m + 20n = -65

15m + 18n = -57

Now, subtracting the second equation from the first equation, we get:

15m + 20n - (15m + 18n) = -65 - (-57)

2n = -8

Dividing both sides by 2, we find that n = -4.

Now, substituting this value of n into one of the original equations, we can solve for m:

3m + 4(-4) = -13

3m - 16 = -13

3m = 3

m = 1.

Therefore, the solution to the system of equations is m = 1 and n = -4.

Answer 2

To solve the system of equations by elimination, multiply the first equation by 5 and the second equation by 3 to make the coefficients of 'm' in both equations opposite. Subtract the second equation from the first equation to eliminate 'm'. The result is 2n = -8. Solve for 'n' by dividing both sides by 2, yielding n = -4. Substitute this value of 'n' back into either of the original equations to solve for 'm'. Using the first equation, substitute -4 for 'n' to get 3m - 16 = -13. Add 16 to both sides to isolate 'm' and get 3m = 3. Divide both sides by 3 to solve for 'm', giving m = 1. Therefore, the solution to the system of equations is m = 1 and n = -4.

Step-by-step explanation:

To solve the system of equations by elimination, multiply the first equation by 5 and the second equation by 3 to make the coefficients of 'm' in both equations opposite. This way, when you add the two equations, the 'm' terms will cancel out. 15m + 20n = -65 and 15m + 18n = -57. Subtract the second equation from the first equation to eliminate 'm'. The result is 2n = -8. Solve for 'n' by dividing both sides by 2, yielding n = -4.

Substitute this value of 'n' back into either of the original equations to solve for 'm'. Using the first equation, substitute -4 for 'n' to get 3m + 4(-4) = -13. Simplify the equation to 3m - 16 = -13. Add 16 to both sides to isolate 'm' and get 3m = 3. Divide both sides by 3 to solve for 'm', giving m = 1.

Therefore, the solution to the system of equations is m = 1 and n = -4.