Solve using the elimination method.
2x/5 + y/2 = 3
x/2-y/6=2
Please and Thank you
I would clean them up first
1st times 10 ----> 4x + 5y = 30
2nd times 6 ----> 3x - y = 12
now multiply that last one by 5
15x - 5y = 60
4x + 5y = 30
Add them:
19x = 90
x = 90/19
y = 3x-12 = 42/19
multiply the first equation by 1/3
2x/15 + y/6 = 1 new first
x/2-y/6=2 second
then add equations
2x/15+x/2=3 then solve for x.
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Multiply both sides of each equation by a coefficient that will make the coefficients of one of the variables the same in both equations.
Looking at the first equation, the coefficients of x and y are 2/5 and 1/2, respectively. To eliminate x, we can multiply both sides of the first equation by 2 to get:
4(2x/5) + 4(y/2) = 4(3)
which simplifies to:
4x/5 + 2y = 12
Now, looking at the second equation, the coefficients of x and y are 1/2 and -1/6, respectively. To eliminate y, we can multiply both sides of the second equation by 6 to get:
6(x/2) - 6(y/6) = 6(2)
which simplifies to:
3x - y = 12
So now we have the system of equations:
4x/5 + 2y = 12
3x - y = 12
Step 2: Multiply one or both equations by coefficients that will make the coefficients of the same variable opposites in each equation.
In this case, we can multiply the second equation by 2 to make the coefficients of y's opposite:
(4x/5 + 2y = 12)
2(3x - y) = 2(12)
This simplifies the second equation to:
6x - 2y = 24
So now we have the system of equations:
4x/5 + 2y = 12
6x - 2y = 24
Step 3: Add the two equations together to eliminate the variable that is now opposites.
Adding the two equations gives us:
(4x/5 + 2y) + (6x - 2y) = 12 + 24
This simplifies to:
4x/5 + 6x = 36
Now, combine the like terms:
(4x + 30x)/5 = 36
Simplifying further gives us:
34x/5 = 36
Step 4: Solve the resulting equation for x.
To do this, multiply both sides of the equation by 5/34:
(5/34)(34x/5) = (5/34)(36)
This simplifies to:
x = 180/34 or x ≈ 5.294
Step 5: Substitute the found value of x back into either of the original equations to solve for y.
Let's use the first equation:
2x/5 + y/2 = 3
Substituting x = 5.294, we have:
2(5.294)/5 + y/2 = 3
Simplifying, we get:
10.588/5 + y/2 = 3
2.118 + y/2 = 3
y/2 = 3 - 2.118
y/2 = 0.882
Now, multiply both sides of the equation by 2 to find y:
2(y/2) = 2(0.882)
y = 1.764
Therefore, the solution to the system of equations is x ≈ 5.294 and y ≈ 1.764.
This completes the solution using the elimination method.