Final answer:
To find the solution of the system of equations -6x-9y=-42 and 6x+5y=10, we can use the method of substitution or the method of elimination. I will use the method of substitution. The solution to the system of equations is x = -50 and y = 60.5.
Step-by-step explanation:
To find the solution of the system of equations -6x-9y=-42 and 6x+5y=10, we can use the method of substitution or the method of elimination. I will use the method of substitution.
Step 1: Solve one equation for one variable.
- Let's solve the second equation, 6x+5y=10, for x: 6x = 10 - 5y
- Divide both sides by 6: x = (10 - 5y) / 6
Step 2: Substitute the expression for x into the other equation.
- Substitute (10 - 5y) / 6 for x in the first equation: -6((10 - 5y) / 6) - 9y = -42
- Multiply every term by 6 to eliminate the fraction: -10 + 5y - 9y = -252
- Combine like terms: -4y - 10 = -252
- Add 10 to both sides: -4y = -242
- Divide both sides by -4: y = 60.5
Step 3: Substitute the value of y back into the expression for x.
- Substitute 60.5 for y in x = (10 - 5y) / 6: x = (10 - 5(60.5)) / 6
- Simplify: x = -50
The solution to the system of equations is x = -50 and y = 60.5.