5x=-3y-9
2x-5y=-16
elimination
set into standard format
5x+3y = -9
2x-5y = -16
Now multiply by proper ratios to eliminate y:
25x+15y = -45
6x-15y = -48
now add to eliminate y:
31x = -93
x = -3
now substitute that value for x into either of the original equations to get y.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by suitable constants such that the coefficients of either x or y in both equations are the same (but with opposite signs).
Let's choose the first equation and multiply it by 2 to make the coefficient of x in both equations the same:
2 * (5x) = 2 * (-3y - 9)
10x = -6y - 18
Now, our system of equations becomes:
10x = -6y - 18
2x - 5y = -16
Step 2: Add or subtract the newly formed equations to eliminate one variable (either x or y).
Let's eliminate y by adding the multiplied version of the first equation to the second equation:
(10x) + (2x - 5y) = (-6y - 18) + (-16)
12x - 5y = -6y - 34
Simplifying, we get:
12x - 5y = -6y - 34
Step 3: Solve the resulting equation for the remaining variable.
Move all terms with y to one side of the equation:
12x - 5y + 6y = -34
12x + y = -34
So the equation becomes:
12x + y = -34.
Now, we have one equation with one variable, so we can solve for x using regular algebraic techniques.
Step 4: Solve for x.
To solve for x, move y to the other side of the equation:
12x + y = -34
12x = -y - 34
Divide all terms by 12:
x = (-y - 34)/12
x = (-1/12)y - 34/12
x = (-1/12)y - 17/6
So the solution to the system of equations is x = (-1/12)y - 17/6.
Note: If you want to find the numerical values of x and y, you would need additional information or equations in order to do so.