5x-y=36
5x+6y=-6
Find the solution in ordered pairs.
5x-y=36
5x+6y=-6
5x-y=36
-1(5x+6y=-6) Distribute
5x-y=36
-5x-6y=6
add these two equations right on top of each other.
0x-7y=42
-7y=42
y=-6
plug in the -6 for y, into either equation, and solve for x.
5x-(-6)=36
5x+6=36
5x=30
x=6
in ordered pairs, the answer is (6,-6)
5x-6y+30=o
To find the solution in ordered pairs for the given system of equations:
Step 1: Start by rearranging the equations in standard form (Ax + By = C), where A, B, and C are integers, and A and B are not both zero.
The given equations are:
5x - y = 36 (Equation 1)
5x + 6y = -6 (Equation 2)
Step 2: Choose one of the equations and isolate one variable in terms of the other. Let's isolate the variable "x" in Equation 1:
5x - y = 36
5x = y + 36
x = (y + 36)/5
Step 3: Substitute the expression for "x" obtained in Step 2 into the other equation. We will use Equation 2:
5x + 6y = -6
5((y + 36)/5) + 6y = -6
y + 36 + 6y = -6
7y + 36 = -6
7y = -6 - 36
7y = -42
y = -42/7
y = -6
Step 4: Substitute the value of "y" (-6) into Equation 1 to solve for "x":
5x - y = 36
5x - (-6) = 36
5x + 6 = 36
5x = 36 - 6
5x = 30
x = 30/5
x = 6
Step 5: Verify the solution by substituting the values of "x" and "y" into the original equations:
Equation 1: 5x - y = 36
5(6) - (-6) = 36
30 + 6 = 36
36 = 36 (True)
Equation 2: 5x + 6y = -6
5(6) + 6(-6) = -6
30 - 36 = -6
-6 = -6 (True)
Step 6: Write the solution as an ordered pair (x, y):
The solution to the system of equations is (6, -6).