5x - 9y = 7,
7y - 3x = -5
solve using any algebraic method
7y-3(9y+7)/5 = -5
y = -1/2
so, x = 1/2
Steve can you explain how you got the answer to this??
sure. the first equation
5x - 9y = 7
tells us that x = (9y+7)/5
Just plug that into the 2nd equation, and you get
7y-3(9y+7)/5 = -5
fractions are a nuisance, so multiply through by 5:
35y - 3(9y+7) = -25
35y - 27y - 21 = -25
8y = -4
y = -1/2
Now plug that value into either equation and solve for x.
To solve the system of equations:
5x - 9y = 7 (Equation 1)
7y - 3x = -5 (Equation 2)
We have a couple of algebraic methods we can use, such as substitution or elimination. Let's use the elimination method:
Step 1: Multiply Equation 1 by 7 and Equation 2 by 5 to eliminate the variable x.
7(5x - 9y) = 7(7)
5(7y - 3x) = 5(-5)
This simplifies to:
35x - 63y = 49 (Equation 3)
35y - 15x = -25 (Equation 4)
Step 2: Now let's multiply Equation 4 by 2 and add it to Equation 3 to eliminate the variable x.
2(35y - 15x) + (35x - 63y) = 2(-25) + 49
This simplifies to:
70y - 30x + 35x - 63y = -50 + 49
7y = -1
Step 3: Solve for y by dividing both sides of the equation by 7:
y = -1/7
Step 4: Substitute the value of y back into one of the original equations. Let's use Equation 1:
5x - 9(-1/7) = 7
5x + 9/7 = 7
Step 5: Solve for x by isolating x to one side of the equation:
5x = 7 - 9/7
5x = 49/7 - 9/7
5x = 40/7
Dividing both sides of the equation by 5:
x = (40/7) / 5
x = 8/7
Therefore, the solution to the system of equations is x = 8/7 and y = -1/7.