How do you solve using the elimination method
0.3x-0.2y=4
0.5x+0.3y=-7/17
To solve using the elimination method, you need to eliminate one variable by adding or subtracting the equations. Here's how you can solve it step by step:
Step 1: Multiply both equations by suitable numbers to clear the decimal. In this case, we can multiply the first equation by 10 and the second equation by 100 to eliminate the decimals. This gives us:
10(0.3x - 0.2y) = 10(4)
100(0.5x + 0.3y) = 100(-7/17)
This simplifies to:
3x - 2y = 40
50x + 30y = -7
Step 2: Now we can eliminate either x or y. Let's eliminate y in this example. Multiply the first equation by 15 and the second equation by 2:
15(3x - 2y) = 15(40)
2(50x + 30y) = 2(-7)
Simplifying gives us:
45x - 30y = 600
100x + 60y = -14
Step 3: Add the two equations together in order to eliminate y:
(45x - 30y) + (100x + 60y) = 600 + (-14)
Simplifying gives us:
(45x + 100x) + (-30y + 60y) = 586
Combining like terms, we get:
145x + 30y = 586
Step 4: Divide the equation by 5 to simplify it further:
29x + 6y = 117.2
Now we have a simplified equation that only involves x and y.
Step 5: Now you have a system of two equations:
29x + 6y = 117.2 ---(1)
3x - 2y = 40 ---(2)
You can solve this system of equations using substitution or elimination method again.
Hope this helps you solve the given system using the elimination method!