how would you solve this with substitution?
-3x – 2y = 16
-x + y = -8
I would say that y = x - 8
then I would say
-3x - 2(x-8) = 16
I would solve that for x
and use that x to go back and find y
from the 2nd, y = x-8
now sub that into the 1st:
-3x - 2(x-8) = 16
-3x - 2x + 16 = 16
-5x = 0
x = 0
y = 0 - 8 = -8
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable.
Let's solve the second equation for x:
-x + y = -8
x = y - 8
Step 2: Substitute the expression for x in the other equation.
Replace x in the first equation with y - 8:
-3(y - 8) - 2y = 16
Step 3: Simplify and solve for y.
Distribute -3:
-3y + 24 - 2y = 16
Combine like terms:
-5y + 24 = 16
Subtract 24 from both sides:
-5y = -8
Divide by -5:
y = 8/5 or 1.6
Step 4: Find the value of x.
Substitute the value of y back into the second equation:
x = 1.6 - 8
x = -6.4
Therefore, the solution is x = -6.4 and y = 1.6.
To solve this system of equations using the method of substitution, you can follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable. For example, let's solve the second equation for y in terms of x:
-x + y = -8
y = x - 8
Step 2: Substitute the expression you obtained in step 1 into the other equation. Replace the variable with the expression.
-3x - 2(x - 8) = 16
Step 3: Simplify and solve for the remaining variable. Distribute the -2 through the parentheses and combine like terms.
-3x - 2x + 16 = 16
-5x + 16 = 16
-5x = 0
x = 0
Step 4: Substitute the value of x back into one of the original equations to find the value of y. Let's use the first equation:
-3(0) - 2y = 16
-2y = 16
y = -8
So, the solution to the system of equations is x = 0 and y = -8.