How do I solve the equations using the elimination method:
.3x-.2y=4 and .4x +.3y= 49/23
Normally I would multiply the decimals by 10 to make them whole numbers, but that fraction is really throwing me off. What do I multiply to eliminate that fraction? Please help!
To solve the given system of equations using the elimination method, let's first try to eliminate the fraction in the second equation.
The fraction in the second equation is 49/23. To eliminate this fraction, we can multiply both sides of the equation by the denominator, which is 23.
By doing this, the second equation becomes:
23 * (0.4x + 0.3y) = 23 * (49/23)
This simplifies to:
9.2x + 6.9y = 49
Now, the system of equations is:
0.3x - 0.2y = 4
9.2x + 6.9y = 49
Now that there are no fractions involved, we can proceed with the elimination method.
To eliminate the variable "y", we need to multiply the first equation by 6.9 and the second equation by 0.2. This will make the coefficients of "y" equal in magnitude but opposite in sign, so they will cancel each other out when added.
So, the modified system of equations is:
(6.9 * 0.3x) - (6.9 * 0.2y) = (4 * 6.9)
(0.2 * 9.2x) + (0.2 * 6.9y) = (0.2 * 49)
Simplifying this, we get:
2.07x - 1.38y = 27.6
1.84x + 1.38y = 9.8
Now, if we add the two equations together, the "y" terms cancel out:
(2.07x - 1.38y) + (1.84x + 1.38y) = 27.6 + 9.8
Simplifying this, we obtain:
3.91x = 37.4
To solve for "x", divide both sides of the equation by 3.91:
x = 37.4 / 3.91
Calculating this value, we have:
x ≈ 9.56
Now that we have the value of "x", we can substitute it back into either of the original equations to find the value of "y".
Let's substitute it into the first equation:
0.3(9.56) - 0.2y = 4
Simplifying this, we get:
2.868 - 0.2y = 4
Next, isolate the "y" term:
-0.2y = 4 - 2.868
-0.2y = 1.132
Finally, solve for "y" by dividing both sides by -0.2:
y = 1.132 / -0.2
Calculating this value, we have:
y ≈ -5.66
Therefore, the solution to the system of equations is approximately x = 9.56 and y = -5.66.