What is the solution for the following system of linear equations?
x + 6y = -4 3x - 4y = 10
from the first equation:
x = -(6y+4)
substitute that for x in the second equation
-3(6y+4) -4y = 10
-18y -12 -4y = 10
-22 y = 22
y = -1
now go back and get x
x = -(6*-1 + 4)
x = - (-2)
x = 2
check
2 + 6*-1 = -4 sure enough
3*2 -4*-1 = 10 yes
To solve the given system of linear equations:
Step 1: We can start by solving one of the equations for one variable in terms of the other variable. Let's solve the first equation for x.
x + 6y = -4
Subtract 6y from both sides:
x = -4 - 6y
Step 2: Now we substitute this expression for x in the second equation.
3x - 4y = 10
Replace x with (-4 - 6y):
3(-4 - 6y) - 4y = 10
Simplify:
-12 - 18y - 4y = 10
Combine like terms:
-12 - 22y = 10
Step 3: Next, we isolate the variable y.
Add 12 to both sides:
-22y = 22
Divide both sides by -22:
y = -1
Step 4: Now we substitute the value of y = -1 back into the equation we found in Step 1 to solve for x.
x = -4 - 6y
Substitute y = -1:
x = -4 - 6(-1)
Simplify:
x = -4 + 6
x = 2
Therefore, the solution to the given system of linear equations is x = 2 and y = -1.
To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the elimination method in this case.
1. The given system of equations is:
x + 6y = -4 (Equation 1)
3x - 4y = 10 (Equation 2)
2. Multiply Equation 1 by 3 to make the coefficients of x in both equations the same. Multiply Equation 2 by 1 to keep the coefficients of x the same. We have:
3(x + 6y) = 3(-4) (Equation 3)
3x - 4y = 10 (Equation 4)
Simplifying Equation 3, we get:
3x + 18y = -12 (Equation 5)
3x - 4y = 10 (Equation 4)
3. Subtract Equation 4 from Equation 5 to eliminate the term "3x":
(3x + 18y) - (3x - 4y) = -12 - 10
Simplifying the equation above gives:
22y = -22
4. Divide both sides of the equation by 22:
y = -1
5. Substitute the value of y = -1 into either Equation 1 or Equation 2 to solve for x. Let's use Equation 1:
x + 6(-1) = -4
Simplifying the equation:
x - 6 = -4
6. Add 6 to both sides of the equation:
x = 2
So, the solution to the system of linear equations is x = 2 and y = -1.