solve by the elimination method
4x+8y=8
-4x+y=10
What is the solution of the system?
Your School Subject is Math or some field of math.
The elimination method is to remove one of the two variable by some linear combinations of the two equations.
In the given case, simply adding together the two equations will eliminate the variable x.
Proceed to solve for y.
Substitute the value of y back into one of the equations to get the value of x.
4x+8y=8
-4x+y=10
Adding together the two equations:
4x-4x+8y+y = 8 + 10
9y = 18
y = 2
Back-substitute y=2 into the first equation:
4x+8(2) = 8
4x+16=8
4x = 8-16=-8
x=-2
Finally, substitute the values x=-2, y=2 into each of the equations to provide a check of the solution.
4(-2)+8(2)=8 OK
-4(-2)+2=10 OK
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a suitable number(s) so that the coefficients of one of the variables will cancel out when the equations are added or subtracted.
In this case, we can multiply the second equation by 4 to eliminate the x term.
-4x + y = 10
(4)(-4x + y) = (4)(10)
-16x + 4y = 40
So, now we have the system of equations:
4x + 8y = 8
-16x + 4y = 40
Step 2: Add or subtract the equations to eliminate one of the variables.
We can eliminate the x variable by adding the two equations together.
(4x + 8y) + (-16x + 4y) = 8 + 40
-12x + 12y = 48
Simplifying the equation gives us:
-12x + 12y = 48
Step 3: Solve the resulting equation for one variable.
Now we have a single equation with only one variable.
-12x + 12y = 48
Let's solve for y by isolating it:
12y = 12x + 48
y = (12x + 48)/12
y = x + 4
Step 4: Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
We can substitute the value of y into the first equation.
4x + 8(x + 4) = 8
4x + 8x + 32 = 8
12x = 8 - 32
12x = -24
x = -24/12
x = -2
Step 5: Substitute the value of x into one of the original equations to find the value of the other variable.
Let's substitute x = -2 into the first equation.
4(-2) + 8y = 8
-8 + 8y = 8
8y = 8 + 8
8y = 16
y = 16/8
y = 2
So, the solution to the system of equations is x = -2 and y = 2.