3x+5y= -11
x-2y= 11
Make the second equation 3x - 6y = 33, and subtract it from the first equation.
That should lead you to
11 y = -44
Take it from there
To solve this system of equations, you can use the method of substitution or the method of elimination. I will explain both methods and then provide a step-by-step solution using the method of substitution.
Method of Substitution:
1. Solve one equation for one variable in terms of the other variable.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for one variable.
4. Substitute the value found back into one of the original equations to solve for the other variable.
5. Write the solution as an ordered pair (x, y).
Method of Elimination:
1. Multiply one or both of the equations by suitable constants to make the coefficients of one of the variables in the two equations equal.
2. Add or subtract the two equations to eliminate one variable.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found back into one of the original equations to solve for the other variable.
5. Write the solution as an ordered pair (x, y).
Now, let's solve the system of equations using the method of substitution:
Step 1: Solve the first equation for x in terms of y:
3x + 5y = -11
3x = -11 - 5y
x = (-11 - 5y) / 3
Step 2: Substitute this expression for x into the second equation:
x - 2y = 11
((-11 - 5y) / 3) - 2y = 11
Step 3: Solve for y:
((-11 - 5y) / 3) - 2y = 11
Multiply through by 3 to eliminate the fraction:
-11 - 5y - 6y = 33
-11 - 11y = 33
-11y = 33 + 11
-11y = 44
y = 44 / -11
y = -4
Step 4: Substitute the value of y back into one of the original equations to solve for x:
3x + 5y = -11
3x + 5(-4) = -11
3x - 20 = -11
3x = -11 + 20
3x = 9
x = 9 / 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = -4, which can be written as the ordered pair (3, -4).