-3x-5y=-6
6x+5y=-34
how do i solve this using elimination?
First you add the equations.
-5y and 5y cross each out so you are left with 3x=-40
X= -40/3
Plug x back into one of the equations
-3x-5y=-6
-3(-40/3)-5y=-6
-40-5y=-6
-5y= 34
Y=34/-5
Correction: It should be positive 40-5y=-6
So -5y=-46
Y=46/5
To solve the system of equations using elimination, we will eliminate one variable by adding or subtracting the equations. Here's a step-by-step guide:
Step 1: Choose a variable to eliminate.
In this case, since the coefficients of the y-term in each equation are already opposites, we can eliminate the variable y.
Step 2: Multiply the equations (if necessary).
In this case, the equations are already in a form where they can be directly added or subtracted.
Step 3: Choose the operation to eliminate the variable.
Since we want to eliminate y, we can add the equations together.
Step 4: Add the equations together.
(-3x - 5y) + (6x + 5y) = (-6) + (-34)
Simplifying,
-3x + 6x - 5y + 5y = -6 - 34
3x = -40
Step 5: Solve for the remaining variable.
Divide both sides of the equation by 3:
3x/3 = -40/3
x = -40/3
Step 6: Substitute the x-value into one of the original equations.
Let's use the first equation:
-3(-40/3) - 5y = -6
40 + 5y = -6
Step 7: Solve for the remaining variable.
Subtract 40 from both sides of the equation:
5y = -46
Step 8: Solve for y.
Divide both sides of the equation by 5:
5y/5 = -46/5
y = -46/5
The solution to the system of equations is x = -40/3 and y = -46/5.