2x+5y=16
5x-2y=11
Please help me solve this system of equations!! I keep getting no solution and i do not know what I am doing wrong.
If you don't even know what one of the variables are, you can't solve the equasion. There IS no solution.
First you multiply the first equation by 5 and the second equation by -2.
You get:
10x+25 = 80
-10x+4y = -22
You cancel out the 10x. Therefore you add the two equations and you get
29y=58
y=2
You plug in 2 for y in any one of the original equations and you get:
x= 3
To solve a system of equations, you need to find the values of x and y that satisfy both equations simultaneously. If you are getting no solution, it means that there is no common solution that satisfies both equations.
Let's go through the process step by step:
1. Begin by rearranging the equations to isolate one variable.
Equation 1: 2x + 5y = 16 --> 2x = 16 - 5y --> x = (16 - 5y)/2
Equation 2: 5x - 2y = 11 --> 5x = 11 + 2y --> x = (11 + 2y)/5
2. Since both equations equal x, we can set them equal to each other, forming an equation in terms of y:
(16 - 5y)/2 = (11 + 2y)/5
3. Now, solve for y. Cross-multiply to get rid of the fractions:
5(16 - 5y) = 2(11 + 2y)
80 - 25y = 22 + 4y
4. Combine like terms:
-25y - 4y = 22 - 80
-29y = -58
5. Divide by -29 to solve for y:
y = (-58)/(-29) = 2
6. Substitute the value of y back into either equation to solve for x. Let's use Equation 1:
2x + 5(2) = 16
2x + 10 = 16
2x = 16 - 10
2x = 6
x = 6/2 = 3
7. Therefore, the solution to the system of equations is x = 3 and y = 2.
It seems there might have been a mistake made along the way when simplifying the equations or solving for y. By following the steps above, you should be able to find the correct solution.