What is the solution? use elimination .
4x-y=23
7x-y=21
You can add both y's together to get no y's and then solve for x after adding 7x and 4x. Then plug in the value of x into one of the equations to find y.
huh?
sorry think of it as you are adding normally with a bar on the bottom. since you have 22 negative y's you multiply the bottom number by -1 to get a positive y. Then you add the two y's together so you ELIMINATE the y's They are no longer in the problem SO FAR. You then find x. and then substitute the answer you got for x and solve y.
sorry typo two negative y's
So whats the answer??
Eq1: 4x - y = 23.
Eq2: 7x - y = 21.
Multiply Eq2 by -1 and add:
+4x - y = 23.
-7x + y = -21.
Sum: -3x = 2.
X = -2/3.
In Eq1, replace x with -2/3 and solve for y.
4(-2/3) - y = 23.
Y = ?
You should get: Y = -77/2 = -25 2/3.
@henry the answer chosies are
a.(11,0)
b.(4,-7)
c.(11,44)
d.(4,7)
None of the give answers satisfy BOTH of
the given equations. Remember that each
answer must satisfy BOTH equations.
My answer: (-2/3,-77/3) satisfies BOTH
equations.
To find the solution using elimination, follow these steps:
Step 1: Write down the given equations:
Equation 1: 4x - y = 23
Equation 2: 7x - y = 21
Step 2: Notice that both equations have the variable "y" with a coefficient of -1. To eliminate "y", subtract Equation 1 from Equation 2. This will result in canceling out the "y" terms:
(7x - y) - (4x - y) = 21 - 23
7x - y - 4x + y = -2
(7x - 4x) - (y - y) = -2
3x = -2
Step 3: Solve the resulting equation for "x":
3x = -2
Divide both sides by 3:
(3x) / 3 = (-2) / 3
x = -2/3
Step 4: Substitute the value of "x" (-2/3) into one of the original equations. Let's use Equation 1:
4x - y = 23
4(-2/3) - y = 23
-8/3 - y = 23
Subtract -8/3 from both sides:
- y = 23 + 8/3
y = 23 + 8/3
Step 5: Simplify the equation for "y":
y = 23 + 8/3
To add fractions, find a common denominator (in this case, 3):
y = (69 + 8) / 3
y = 77 / 3
The solution to the system of equations is x = -2/3 and y = 77/3.