Hello any one out there can you please help me out with this problem and Thank you in advance.
!.x+y=34
x-y=20
2.-7x+6y=11
-5x+9y-11
#1
Since y = 34-x,
x-(34-x) = 20
2x = 54
x = 27
y = 7
#2
There's a typo. If you meant to say
-5x+9y = 11,
do a little multiplying to get rid of y:
-21x+18y = 33
-10x+18y = 22
-11x = 11
x = -1
y = 2/3
If it was -5x+9y = -11, then
x = -5
y = -4
Thank you so much.
Of course, I can help you with these problems!
1. To solve the system of equations:
Equation 1: x + y = 34
Equation 2: x - y = 20
There are multiple methods you can use, but I'll explain how to solve it using the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve Equation 2 for x:
x = y + 20
Step 2: Substitute the expression obtained in Step 1 into the other equation.
Substitute x = y + 20 (from Step 1) into Equation 1:
(y + 20) + y = 34
Step 3: Solve the resulting equation for y.
2y + 20 = 34
2y = 34 - 20
2y = 14
y = 14/2
y = 7
Step 4: Substitute the value of y back into the expression from Step 1 to find x.
x = y + 20
x = 7 + 20
x = 27
Thus, the solution to the system of equations is x = 27 and y = 7.
2. To solve the system of equations:
Equation 1: -7x + 6y = 11
Equation 2: -5x + 9y - 11 = 0
Again, there are multiple methods to solve this system, but I'll explain how to use the method of elimination.
Step 1: Multiply both sides of Equation 2 by -6 to make the coefficients of x in both equations equal.
-6 * (-5x + 9y - 11) = -6 * 0
30x - 54y + 66 = 0
Now we have:
Equation 1: -7x + 6y = 11
Equation 2: 30x - 54y + 66 = 0
Step 2: Add the two equations together to eliminate the y variable.
(-7x + 6y) + (30x - 54y) = 11 + 66
23x - 48y = 77
Step 3: Solve the resulting equation for x or y. Let's solve it for x.
23x = 48y + 77
x = (48y + 77)/23
Step 4: Substitute the expression obtained in Step 3 into either of the original equations to solve for y.
Let's substitute x = (48y + 77)/23 into Equation 1:
-7((48y + 77)/23) + 6y = 11
Simplify the equation and solve for y.
Once you have the value of y, substitute it back into the expression from Step 3 to find x.
I hope this explanation helps you solve the given systems of equations! If you have any further questions, please let me know.