0.3x-0.2y=4
0.5x+0.3y=-7/17
Can anyone Please help me solve using the elimination system.....
multiply the entire first line by (3/2)
0.3x(3/2) -0.2y(3/2)=4(3/2)
0.5x+0.3y=-7/17
and get
0.45x -0.3y =6
0.5x + 0.3y =-7/17
---------------------subtract
-0.05x = 6 7/17
-.05 x = 109/17
solve for x and go back and get y
See my above answer. Elimination as a process pretty much works the same no matter what, even if what you have to work with is a little ugly.
This is very confusing I do not get it
I multiplied the first equation, all terms by 3/2 to get o.3 in front of y in both equations
0.3x(3/2) -0.2y(3/2)=4(3/2)
0.5x+0.3y=-7/17
and get
0.45x -0.3y =6
0.5x + 0.3y =-7/17
---------------------add
.95 x = 95/17
To solve the given system of equations using elimination, follow these steps:
1. Multiply one or both equations by appropriate constants so that the coefficients of one of the variables will cancel out when the two equations are added or subtracted.
2. Add or subtract the two equations to eliminate one variable and obtain a new equation with only one variable.
3. Solve the new equation for the remaining variable.
4. Substitute the value of the variable found in the previous step back into one of the original equations to find the value of the other variable.
Here's how you can use elimination to solve the given system of equations:
Equation 1: 0.3x - 0.2y = 4 ...(i)
Equation 2: 0.5x + 0.3y = -7/17 ...(ii)
To eliminate the y term, we can multiply equation (i) by 1.5 and equation (ii) by 0.6, which will make the coefficients of the y terms equal:
1.5 * (0.3x - 0.2y) = 1.5 * 4
0.6 * (0.5x + 0.3y) = 0.6 * (-7/17)
Simplifying the equations:
0.45x - 0.3y = 6 ...(iii)
0.3x + 0.18y = -14/17 ...(iv)
Now, we can add equations (iii) and (iv) to eliminate the y term:
(0.45x - 0.3y) + (0.3x + 0.18y) = 6 + (-14/17)
Combine like terms on both sides:
0.45x + 0.3x - 0.3y + 0.18y = 6 - 14/17
0.75x - 0.12y = 6 - 14/17
To simplify further, convert the mixed number on the right side into a fraction:
0.75x - 0.12y = 102/17 - 14/17
0.75x - 0.12y = 88/17
Now, we have a new equation:
0.75x - 0.12y = 88/17 ...(v)
Next, we can solve equation (v) for the variable x:
0.75x = 0.12y + 88/17
Divide both sides by 0.75:
x = (0.12y + 88/17) / 0.75
Now, we have the value of x in terms of y.
To find the value of y, substitute the value of x in the original equation (i):
0.3x - 0.2y = 4
0.3[(0.12y + 88/17) / 0.75] - 0.2y = 4
Simplify this equation and solve for y.
Once you find the value of y, you can substitute it back into equation (i) or equation (ii) to find the value of x.
Remember to double-check your solutions by plugging them back into both original equations to ensure they satisfy both equations.