How to use an elimination strategy to solve the linear system:
5/3x +1/4y = 10
1/3x + 1/2y = 5
since 1/2 is 2(1/4), multiply the top by 2o to get
10/3 x + 1/2 y = 20
Then 1/2 y = 20 - 10/3 x
Plug that into the 2nd equation and you have
1/3 x + (20 - 10/3 x) = 5
X= -5/9
To use the elimination strategy to solve a linear system of equations, follow these steps:
Step 1: Multiply both equations by suitable constants to eliminate one variable. In this case, we can multiply the first equation by 12 to eliminate the fractions, and the second equation by 6 to also eliminate the fractions.
The first equation becomes: (12)(5/3x) + (12)(1/4y) = (12)(10)
This simplifies to: 20x + 3y = 120
The second equation becomes: (6)(1/3x) + (6)(1/2y) = (6)(5)
This simplifies to: 2x + 3y = 30
Step 2: Subtract one equation from the other to eliminate one variable. Since both equations now have the same coefficient for the 'y' term, we can subtract the second equation from the first equation.
(20x + 3y) - (2x + 3y) = 120 - 30
This simplifies to: 18x = 90
Step 3: Solve the new equation obtained in step 2 for the remaining variable. In this case, divide both sides of the equation by 18.
18x = 90
x = 90/18
x = 5
Step 4: Substitute the value of the variable found in step 3 into either of the original equations to solve for the other variable. Let's substitute it into the second equation.
2(5) + 3y = 30
10 + 3y = 30
3y = 30 - 10
3y = 20
y = 20/3
y = 6.67 (rounded to two decimal places)
So, the solution to the linear system of equations is x = 5 and y = 6.67.