10x - 2y = 16 and x +5y = -20
since x = -20-5y,
10(-20-5y) - 2y = 16
Solve for y, then get x
To solve this system of linear equations:
1. Method: Substitution
- Start with the second equation, x + 5y = -20, and solve for x in terms of y:
x = -20 - 5y
- Substitute the value of x in the first equation: 10(-20 - 5y) - 2y = 16
- Simplify the equation:
-200 - 50y - 2y = 16
-52y = 216
- Solve for y:
y = -216 / -52
y = 4.15 (rounded to two decimal places)
- Substitute the value of y back into the second equation to solve for x:
x + 5(4.15) = -20
x + 20.75 = -20
x = -40.75
Therefore, the solution to the system of equations is x = -40.75 and y = 4.15.
2. Method: Elimination
- Multiply the first equation by 5 to make the coefficients of y in both equations equal:
50x - 10y = 80
- Multiply the second equation by 2 to make the coefficients of x in both equations equal:
2x + 10y = -40
- Add the two equations together to eliminate y:
50x - 10y + 2x + 10y = 80 + (-40)
52x = 40
- Solve for x:
x = 40 / 52
x = 0.77 (rounded to two decimal places)
- Substitute the value of x back into either of the original equations to solve for y. Let's use the second equation:
0.77 + 5y = -20
5y = -20 - 0.77
5y = -20.77
y = -20.77 / 5
y = -4.15 (rounded to two decimal places)
Therefore, the solution to the system of equations is x = 0.77 and y = -4.15.