-3x + 2y = 8
x + 4y = -4
use substitution method to solve the linear system.
-3x + 2y = 8
x + 4y = -4
x + 4y = -4
x = -4 - 4y
Substitute, x = -4 - 4y in,
-3x + 2y = 8
-3(-4 - 4y) + 2y = 8
12 + 12y + 2y = 8
14y = -4
y = -4/14
y = -2/7
Substitute, y = -2/7 in either equation to find x.
Then check your solutions in the original equations.
To solve the linear system using the substitution method, we can start by solving one equation for one variable and then substituting that expression into the other equation. Let's solve the second equation for x:
x + 4y = -4
We can isolate x by subtracting 4y from both sides:
x = -4 - 4y
Now, we substitute this expression for x into the first equation:
-3x + 2y = 8
-3(-4 - 4y) + 2y = 8
Simplifying this equation gives:
12 + 12y + 2y = 8
Combine like terms:
14y + 12 = 8
Subtract 12 from both sides:
14y = -4
Divide by 14:
y = -4/14
Simplifying this expression gives:
y = -2/7
Now, substitute this value of y back into the expression for x:
x = -4 - 4y
x = -4 - 4(-2/7)
Simplifying this equation gives:
x = -4 + 8/7
To add these fractions, we need a common denominator:
x = (-28/7 + 8/7) / 1
Simplifying this equation gives:
x = (-20/7) / 1
Dividing these fractions gives:
x = -20/7
Therefore, the solution to the linear system is:
x = -20/7 and y = -2/7.
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute it into the other equation. Let's solve the second equation for x in terms of y.
x + 4y = -4 (equation 1)
Solving equation 1 for x:
x = -4 - 4y (equation 2)
Now we substitute equation 2 into the first equation:
-3(-4 - 4y) + 2y = 8
Distribute -3 to the terms inside the parentheses:
12 + 12y + 2y = 8
Combining like terms:
14y + 12 = 8
Subtracting 12 from both sides:
14y = -4
Dividing both sides by 14:
y = -4/14
Simplifying:
y = -2/7
Now that we have the value of y, we can substitute it back into equation 2 to solve for x:
x = -4 - 4(-2/7)
Simplifying:
x = -4 + 8/7
x = -28/7 + 8/7
x = -20/7
Therefore, the solution to the system of equations is x = -20/7 and y = -2/7.