using cross multiplication method solve 3x+5y=25 , 7x+6y=30
Maybe means multiply first one by 7 and second one by 3 ?
I doubt if they have gotten to Cramer or Gauss Jordan.
21 x + 35 y = 175
21 x + 18 y = 90
---------------------subtract
0 x + 17 y = 85
y = 5
then x = 0
huh? do you mean solving by matrix crammers rule?
To solve the system of equations 3x + 5y = 25 and 7x + 6y = 30 using the cross multiplication method, follow these steps:
Step 1: Rearrange one equation
Choose one equation to rearrange in the form y = mx + b, where m represents the coefficient of x and b represents the constant term.
Let's choose the first equation, 3x + 5y = 25.
Rearranging for y, we get 5y = -3x + 25.
Dividing both sides by 5, we have y = (-3/5)x + 5.
Step 2: Cross multiply
Take the equation obtained from step 1, y = (-3/5)x + 5, and multiply both sides by the coefficient of the x-term in the other equation.
In this case, we multiply both sides of this equation by 6 (the coefficient of x in the second equation) to get rid of the fraction.
6y = (-3/5)(6x) + 6(5).
Simplifying, we get 6y = -18/5 x + 30.
Step 3: Set the two equations equal to each other
The next step is to set the two equations equal to each other. So, equate the two expressions obtained from step 2.
(-18/5)x + 30 = -3x + 25.
Step 4: Solve for x
Solve the equation obtained in step 3 for x.
Start by isolating x on one side of the equation.
Add 3x to both sides:
(-18/5)x + 3x + 30 = 25 + 3x.
Combining like terms, we have:
(-18/5 + 3)x + 30 = 25 + 3x.
(-18/5 + 15/5)x + 30 = 25 + 3x.
(-3/5)x + 30 = 25 + 3x.
Next, subtract 3x from both sides:
(-3/5)x + 30 - 3x = 25 + 3x - 3x.
(-3/5 - 15/5)x + 30 = 25 + 0.
(-18/5)x + 30 = 25.
Subtract 30 from both sides to isolate the x-term:
(-18/5)x + 30 - 30 = 25 - 30.
(-18/5)x = -5.
Finally, multiply both sides by -5/18 (the reciprocal of -18/5) to solve for x:
((-5/18)(-18/5))x = (-5/18)(-5).
x = 5/18.
Step 5: Substitute x into one of the original equations
Now that you have found the value of x, substitute it back into one of the original equations to solve for y.
Let's use the first equation, 3x + 5y = 25.
Substituting x = 5/18, we have:
3(5/18) + 5y = 25.
Simplifying, we get:
(15/18) + 5y = 25.
Multiplying through by 18 to eliminate the fraction, we have:
15 + 90y = 450.
Subtracting 15 from both sides, we get:
90y = 435.
Dividing by 90, we have:
y = 435/90.
Step 6: Simplify the solution
Simplify the results obtained in step 5 to get the final solution.
x = 5/18
y = 435/90.
If desired, you can further simplify the fractions or convert them to decimals or mixed numbers.