Solve by the elimination method
0.3x-0.2y=4
0.4x+0.5y= - 55/17
Thank you
multiply the first equation by 5, the second equation by2
1.5x-y=20
.8x+y=-110/17
add the equations
2.3x=20-110/17
multipy both sides by 17
39.1x=340-110
x= 230/39.1
To solve the system of equations by the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant(s) to make the coefficients of one of the variables equal. In this case, we can multiply the first equation by 10 to eliminate the decimal:
10(0.3x - 0.2y) = 10(4)
This simplifies to:
3x - 2y = 40
The second equation remains the same:
0.4x + 0.5y = -55/17
Step 2: You need to eliminate one of the variables, either x or y. In this case, let's eliminate the y-variable. To do this, multiply both sides of the first equation by 5, and multiply both sides of the second equation by 2:
5(3x - 2y) = 5(40)
2(0.4x + 0.5y) = 2(-55/17)
This simplifies to:
15x - 10y = 200
0.8x + y = -110/17
Step 3: Add the two modified equations together to cancel out the variable being eliminated. In this case, we will add the two equations as follows:
(15x - 10y) + (0.8x + y) = (200) + (-110/17)
This simplifies to:
15.8x - 9y = 200 - (110/17)
To get rid of the decimal and fraction, multiply everything by 17:
(15.8x - 9y) * 17 = (200 - (110/17)) * 17
This simplifies to:
268.6x - 153y = 3400 - 110
Step 4: Simplify and continue solving for x and y.
The new system of equations is:
15.8x - 9y = 3400 - 110
15x - 10y = 200
Now, we have two equations in x and y. You can solve it further using the same method or any other method you prefer, such as substitution or matrix methods.