solve each system by substitution method
x=y+3
3x-2y=4
Pls determine whether the equations are independent, dependent, or inconsistent
x=y+3
3x-2y=4
Substitute y+3 for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson
To solve the system of equations using the substitution method, we need to isolate one variable in one of the equations and then substitute that expression into the other equation.
Given the system of equations:
1) x = y + 3
2) 3x - 2y = 4
Step 1: Solve Equation 1 for x:
x = y + 3
Step 2: Substitute the value of x from Equation 1 into Equation 2:
3(y + 3) - 2y = 4
Simplify equation 2:
3y + 9 - 2y = 4
y + 9 = 4
y = 4 - 9
y = -5
Step 3: Substitute the value of y = -5 into Equation 1 to find x:
x = (-5) + 3
x = -2
Therefore, the solution to the system of equations is x = -2 and y = -5.
To determine whether the equations are independent, dependent, or inconsistent, we need to check if the solution satisfies both equations.
Substituting the values of x and y into both equations:
1) -2 = -5 + 3 -> -2 = -2 (True)
2) 3(-2) - 2(-5) = 4 -> -6 + 10 = 4 -> 4 = 4 (True)
The solution (-2, -5) satisfies both equations, indicating that the system of equations is consistent and dependent because there is only one possible solution.