How do I solve for elimination method on this problem: 0.3x - 0.2y=4 and 0.3x + 0.3y= 5/19. I know that multiply by 10 on both equations and get 3x-2y=40 and 3x+3y=50/19. and then I have to multiply 3x-3y=40 by 3 and 3x+3y= 50/19 by -3 to get 9x-9y=120 and -9x-9y=-150/19. But from there I get lost. Can someone please help me?
I just did your earlier problem. Please study that. If you can do one you can do them all.
first if you have .3 x in both, why multiply by 10?
.3 x - .2 y = 4
.3 x + .3 y = 5/19
subtract second from first
0 x - .5 y = 71/19
y = - 142/19
so
.3 x - .2 (-142/19) = 40
3 x = -2(142/19) + 760/19
3 x = 476/19
x = 476/57
To solve the system of equations using the elimination method, you can eliminate one variable by adding or subtracting the equations. In this case, you can eliminate the y variable.
Step 1: Multiply the first equation by 3 and the second equation by -2 to get:
3x - 2y = 40
-2(3x + 3y) = -2(5/19)
Simplify the second equation:
-6x - 6y = -10/19
Step 2: Add the two equations together to eliminate the y variable:
(3x - 2y) + (-6x - 6y) = 40 + (-10/19)
Simplify:
-3x - 8y = 40 - 10/19
Step 3: To isolate the x variable, multiply the equation by -1:
-1(-3x - 8y) = -1(40 - 10/19)
Simplify:
3x + 8y = -40 + 10/19
Step 4: Add this new equation to the original second equation:
(3x + 8y) + (3x + 3y) = -40 + 10/19 + 50/19
Simplify:
6x + 11y = 10/19
Now you have another equation with only x and y variables.
Step 5: Now you can solve the system of equations formed by the equations from Step 2 and Step 4.
-3x - 8y = 40 - 10/19
6x + 11y = 10/19
To eliminate the x variable, multiply the second equation by 2 and the first equation by 3:
(6x + 11y) + 2(-3x - 8y) = (10/19) + 2(40 - 10/19)
Simplify:
6x + 11y - 6x - 16y = 10/19 + 80 - 20/19
Simplify further:
-5y = 810/19 - 200/19
Step 6: Solve for y by simplifying the equation:
-5y = 610/19
Divide both sides by -5:
y = (610/19) / -5
Simplify:
y = -122/19
Step 7: Substitute the value of y back into either of the earlier equations to solve for x. Let's use the first equation:
0.3x - 0.2(-122/19) = 4
Simplify:
0.3x + (24.4/19) = 4
Subtract (24.4/19) from both sides:
0.3x = 4 - (24.4/19)
Simplify:
0.3x = (76 - 24.4)/19
Divide both sides by 0.3:
x = [(76 - 24.4)/19] / 0.3
Simplify:
x = (51.6/19) / 0.3
x = 51.6/19 * 10/3
x = 172/19
So, the solution to the system of equations is x = 172/19 and y = -122/19.