Solve the system of equations by the elimination method 9/x++3/8y=-9/4 and -1/9x+5/4y=1/9
first step is usually to get rid of the nasty fractions. I see there's a typo in the first equation. I'll just assume 9/4 x. If wrong, fix it and follow the same steps to solution.
18x + 3y = -18
-4x + 45y = 4
or
6x + y = -6
-4x + 45y = 4
multiply to get rid of x:
12x + 2y = -12
-12x + 135y = 12
Now add the two equations to get
137y = 0
y = 0
so, x = -1
If I made the wrong guess, fix it and follow similar steps to solution.
To solve the system of equations using the elimination method, we need to eliminate one variable by manipulating the equations and then solve for the remaining variable.
Let's start by eliminating the x variable. We can do this by multiplying the first equation by 9 and the second equation by 8 to make the coefficients of x to be opposites of each other.
Multiplying the first equation by 9:
9 * (9/x) + 9 * (3/8y) = 9 * (-9/4)
81/x + 27/8y = -81/4
Multiplying the second equation by 8:
8 * (-1/9x) + 8 * (5/4y) = 8 * (1/9)
-8/9x + 10/9y = 8/9
Now we have the following system of equations:
81/x + 27/8y = -81/4
-8/9x + 10/9y = 8/9
To eliminate the x variable, we need to make the coefficients of x in both equations equal. To do this, we can multiply the first equation by -8/9 and the second equation by 81.
Multiplying the first equation by -8/9:
(-8/9) * (81/x) + (-8/9) * (27/8y) = (-8/9) * (-81/4)
-72/x + (-24/8)y = 72/4
Multiplying the second equation by 81:
81 * (-8/9x) + 81 * (10/9y) = 81 * (8/9)
-64x + 90y = 72
Now we have the following system of equations:
-72/x - 24/8y = 72/4
-64x + 90y = 72
Next, we can add the two equations together to eliminate the x variable:
(-72/x + -24/8y) + (-64x + 90y) = (72/4) + 72
-72/x - 24/8y - 64x + 90y = 288/4 + 72
Simplifying:
-72/x - 3y - 64x + 90y = 288/4 + 72
-64x - 72/x - 3y + 90y = 72 + 72
Combining terms:
-64x - 72/x + 87y = 144
Now, we have one equation with one variable remaining. Let's solve for y:
-64x - 72/x + 87y = 144
To get the x term and the y term on one side of the equation, we can move the -64x - 72/x term to the other side:
87y = 64x + 72/x - 144
To simplify further, we can find a common denominator for 72/x and 144:
87y = (64x^2 + 72 - 144x) / x
Now, we can simplify the equation by multiplying both sides by x:
87xy = 64x^2 + 72 - 144x
Rearranging the equation:
64x^2 - 144x - 87xy + 72 = 0
At this point, it becomes a quadratic equation. To solve for x or y, we need additional information such as the value of x or y from either of the original equations. Unfortunately, the original equations provided do not contain any specific values for x or y, making it impossible to find exact solutions.
Therefore, the system of equations cannot be solved using the elimination method without additional information.