solve the following simultaneous equation:
5x+2y=29
x-y=-4
2x-y=-1
3x-y=2
5x+y=16
x-2y=1
5x+2y=16
-3x+4y=-7
3x+2y=19
5x-2y=5
7x-1/3-2(7y+3)/5=10/3
5x+2/4+3y-2/5=16/5
I'll show you how to do the first oner. You try the others using the same method.
5x +2y = 29
x - y = -4
Double the last equation (both sides)
2x -2y = -8
Add the first and third equations.
7x = 21
x = 3
To solve a system of simultaneous equations, we can use the method of substitution or the method of elimination. I will explain both methods, and you can choose which one you prefer to use.
1. Method of substitution:
In this method, we solve one equation for one variable and substitute the expression into the other equation. Let's use this method for the first example:
Equation 1: 5x + 2y = 29
Equation 2: x - y = -4
Solve Equation 2 for x:
x = -4 + y
Substitute x into Equation 1:
5(-4 + y) + 2y = 29
-20 + 5y + 2y = 29
7y = 49
y = 7
Now substitute y back into Equation 2 to find x:
x = -4 + 7
x = 3
Therefore, the solution to the first simultaneous equation is x = 3, y = 7. You can apply the same method to solve the remaining examples.
2. Method of elimination:
In this method, we eliminate one variable by adding or subtracting the equations. We will multiply the equations by suitable constants to make the coefficients of one variable the same.
Let's use this method for the second example:
Equation 1: 2x - y = -1
Equation 2: 3x - y = 2
Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the variable y:
3(2x - y) = 3(-1)
2(3x - y) = 2(2)
Simplifying:
6x - 3y = -3
6x - 2y = 4
Subtract the two equations to eliminate x:
(6x - 3y) - (6x - 2y) = -3 - 4
-y = -7
y = 7
Substitute y back into either equation to find x:
2x - 7 = -1
2x = 6
x = 3
So the solution is x = 3, y = 7.
You can apply the same method to solve the remaining examples.
Note: For the last two examples you provided, they seem to have missing information or formatting issues. If you can clarify the equations, I can explain how to solve them as well.