solve using the substitution method:
8x+5y=-12
x=12-4y
x=12-4y
8x+5y= -12
8*(12-4y)+5y= -12
8*12-8*4y+5y= -12
96-32y+5y= -12
96-27y= -12
96+12=27y
108=27y Divide with 27
4=y
y=4
x=12-4y
x=12-4*4
x=12-16
x= -4
To solve the system of equations using the substitution method, we'll follow these steps:
Step 1: Solve one equation for one variable.
Step 2: Substitute the solved variable into the other equation.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
Step 5: Check the solution in both original equations.
Let's start solving the system of equations using the substitution method:
Given equations:
1) 8x + 5y = -12
2) x = 12 - 4y
Step 1: Solve equation 2) for x:
x = 12 - 4y
Step 2: Substitute the value of x from equation 2) into equation 1):
8(12 - 4y) + 5y = -12
Step 3: Simplify and solve the resulting equation for y:
96 - 32y + 5y = -12
(96 - 12) - 32y + 5y = 0
84 - 27y = 0
-27y = -84
y = 84/27
y ≈ 3.11
Step 4: Substitute the value of y back into equation 2) to solve for x:
x = 12 - 4(3.11)
x ≈ 12 - 12.44
x ≈ -0.44
Step 5: Check the solution in both original equations:
Checking equation 1):
8(-0.44) + 5(3.11) = -12
-3.52 + 15.55 ≈ -12
12.03 ≈ -12 (approximately equal)
Checking equation 2):
-0.44 = 12 - 4(3.11)
-0.44 ≈ 12 - 12.44
-0.44 ≈ -0.44 (approximately equal)
The solution to the system of equations is approximately x = -0.44 and y ≈ 3.11.