i need help with this problem x AND y ARE THE SAME IN BOTH PROBLEM????
7x+8y=25
9x+10Y=35
7x+8y=25 times 5 is 35 x + 40 y = 125
9x+10y=35 times 4 is 36 x + 40 y = 140
++++++++++++++++++++++now subtract
-1 x + 0 = -15
so
x = 15
then
7(15) + 8 y = 25
105 + 8 y = 25
8 y = -80
y = -10
thanks but y\why did you multiply it by 4 and 5 at the begging
Because 40 is the least common multiple of 8 and 10
I could have used the first times 9 and the second times 7 and eliminated x.
What method is this (like is it elimination,substiution)
To determine if x and y are the same in both equations, we need to solve the system of equations by finding the values of x and y that satisfy both equations simultaneously.
First, let's solve the system using the method of substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
7x + 8y = 25
7x = 25 - 8y
x = (25 - 8y) / 7
Step 2: Substitute this expression for x into the second equation.
9x + 10y = 35
9((25 - 8y) / 7) + 10y = 35
Now we can solve for y:
Step 3: Distribute the 9 to the terms inside the parentheses:
(9 * 25 - 9 * 8y) / 7 + 10y = 35
(225 - 72y) / 7 + 10y = 35
Step 4: Multiply everything by 7 to clear the fraction:
225 - 72y + 70y = 245
-2y = 20
y = -10
Now that we have the value for y, we can substitute it back into one of the equations to find x:
Step 5: Substitute y = -10 into either of the original equations. Let's use the first equation:
7x + 8(-10) = 25
7x - 80 = 25
7x = 105
x = 15
The solution to the system of equations is x = 15 and y = -10.
To answer your initial question, in this system of equations, x and y are not the same value.