solve using any method and identify the system as consistent, inconsistent or dependent. 3x-4y=8
6x-2y=10
I want to use elimination. this is taking me forever!
Why use "elimination", it is perfectly set up for substitution.
4y = 8
y = 2
sub that into the other equation, ....
6x - 2(2) = 10
6x = 14
x = 14/6 = 7/3
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both of the equations by appropriate constants to make the coefficients of one of the variables the same or multiples of each other.
In this case, let's multiply the second equation by 2 so that the coefficients of y in both equations become opposites:
3x - 4y = 8
12x - 4y = 20
Step 2: Add or subtract the equations to eliminate one of the variables.
Subtract the first equation from the second equation:
12x - 4y - (3x - 4y) = 20 - 8
This simplifies to:
9x = 12
Step 3: Solve the resulting equation for the remaining variable.
Divide both sides of the equation by 9:
x = 12/9
x = 4/3
Step 4: Substitute the value found in step 3 back into either of the original equations to find the value of the other variable.
Let's substitute x = 4/3 into the first equation:
3(4/3) - 4y = 8
4 - 4y = 8
Subtract 4 from both sides:
-4y = 8 - 4
-4y = 4
Divide both sides by -4:
y = -4/4
y = -1
Step 5: Check the solution by substituting the values of x and y into both original equations.
Substituting x = 4/3 and y = -1 into the first equation:
3(4/3) - 4(-1) = 8
4 - (-4) = 8
4 + 4 = 8
8 = 8 (true)
Substituting x = 4/3 and y = -1 into the second equation:
6(4/3) - 2(-1) = 10
8 - (-2) = 10
8 + 2 = 10
10 = 10 (true)
Since both equations are true, the system is consistent and the solution is x = 4/3 and y = -1.