2x +5y=0
3x -2y=19
To find the solution of the system of equations:
2x + 5y = 0
3x - 2y = 19
We can use either substitution or elimination method. Here's how to solve it using the elimination method:
1. Multiply the first equation by 2 to get rid of the coefficient of x:
4x + 10y = 0
2. Multiply the second equation by 5 to get rid of the coefficient of y:
15x - 10y = 95
3. Add the two equations together:
4x + 10y = 0
+ 15x - 10y = 95
______________
19x = 95
4. Solve for x:
x = 5
5. Substitute x = 5 into the first equation to solve for y:
2x + 5y = 0
2(5) + 5y = 0
10 + 5y = 0
5y = -10
y = -2
Therefore, the solution to the system of equations is (x, y) = (5, -2).
To solve this system of equations, you can use the method of substitution or the method of elimination. I will demonstrate 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:
2x + 5y = 0
Subtract 5y from both sides:
2x = -5y
Divide both sides by 2:
x = -5y/2
Step 2: Substitute the expression for x into the other equation.
Now replace x in the second equation with -5y/2:
3x - 2y = 19
3(-5y/2) - 2y = 19
Step 3: Simplify and solve for y.
Multiply 3 and (-5y/2):
-15y/2 - 2y = 19
-15y - 4y = 38
Combine like terms:
-19y = 38
Divide both sides by -19:
y = 38/-19
y = -2
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's use the first equation:
2x + 5y = 0
2x + 5(-2) = 0
2x - 10 = 0
Add 10 to both sides:
2x = 10
Divide both sides by 2:
x = 10/2
x = 5
Step 5: Check the solution.
Plug the values of x and y back into both equations to make sure they satisfy both equations:
2(5) + 5(-2) = 0
10 - 10 = 0
0 = 0 (True)
3(5) - 2(-2) = 19
15 + 4 = 19
19 = 19 (True)
Therefore, the solution to the system of equations is x = 5 and y = -2.