what is the solution to the above system of equation 2x + 5y =-4
4x -5y =22
(3,-2)
Oh boy, these equations seem to be in a bit of a circus! Let me see if I can entertain you with the solution. 🎪
We can solve this system of equations by using the method of elimination or substitution. Since the coefficients of the y-term in both equations have the same magnitude but opposite signs, we can add the equations together to eliminate the y terms.
When we add the equations, 2x + 4x will give us 6x, and -5y + (-5y) will give us -10y. On the right side, -4 + 22 will give us 18.
So the new equation we get is 6x - 10y = 18. Now, let me juggle some numbers around to solve for one of the variables.
If we divide the equation by 2, we get 3x - 5y = 9. Now we have a new equation that we can use to substitute into one of the original equations. Let's substitute the value of 3x - 5y into the second equation.
Plugging in the value, we get 4x - 5(9) = 22. Time to do some clown math!
4x - 45 = 22. Adding 45 to both sides, we get 4x = 67. Dividing both sides by 4, we find that x = 16.75.
Now, we can substitute this value back into one of the original equations to find y. How about we use the first equation?
Putting in the value of x, we have 2(16.75) + 5y = -4. Time to juggle some numbers again!
33.5 + 5y = -4. Subtracting 33.5 from both sides, we have 5y = -37.5. Dividing both sides by 5, we find that y = -7.5.
So, the solution to this circus of equations is x = 16.75 and y = -7.5. Ta-da! 🎉
To find the solution to the given system of equations, we will use the method of elimination.
Step 1: Multiply the first equation by 4 and the second equation by 2 to eliminate the y variable.
4(2x + 5y) = 4(-4)
2(4x - 5y) = 2(22)
Simplifying these equations, we get:
8x + 20y = -16
8x - 10y = 44
Step 2: Subtract the second equation from the first equation to eliminate the x variable.
(8x + 20y) - (8x - 10y) = -16 - 44
Simplifying this equation, we get:
30y = -60
Step 3: Divide both sides of the equation by 30 to solve for y.
y = -60/30
y = -2
Step 4: Substitute the value of y back into one of the original equations to solve for x.
2x + 5(-2) = -4
Simplifying this equation, we get:
2x - 10 = -4
Step 5: Add 10 to both sides of the equation.
2x = -4 + 10
2x = 6
Step 6: Divide both sides of the equation by 2 to solve for x.
x = 6/2
x = 3
Therefore, the solution to the given system of equations is x = 3 and y = -2.
To find the solution to the system of equations, we can use the method of elimination or substitution. I will explain both methods, and you can choose which one you prefer.
Method 1: Elimination
Step 1: Multiply the first equation by 4 and the second equation by 2 to make the y-coefficient in both equations the same:
Equation 1: 8x + 20y = -16
Equation 2: 8x - 10y = 44
Step 2: Subtract Equation 2 from Equation 1 to eliminate the x-term:
(8x + 20y) - (8x - 10y) = (-16) - (44)
8x - 8x + 20y + 10y = -16 - 44
30y = -60
Step 3: Divide both sides of the equation by 30:
30y/30 = -60/30
y = -2
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Using Equation 1: 2x + 5(-2) = -4
2x - 10 = -4
2x = -4 + 10
2x = 6
x = 3
Therefore, the solution to the system of equations is x = 3 and y = -2.
Method 2: Substitution
Step 1: Solve one of the equations for one variable.
We will solve Equation 2 for x:
4x - 5y = 22
4x = 22 + 5y
x = (22 + 5y) / 4
Step 2: Substitute the expression for x into the other equation and solve for y.
Substituting x = (22 + 5y) / 4 into Equation 1:
2((22 + 5y) / 4) + 5y = -4
Simplifying the equation:
(22 + 5y)/2 + 5y = -4
22 + 5y + 10y = -8
22 + 15y = -8
15y = -8 - 22
15y = -30
y = -2
Step 3: Substitute the value of y back into one of the original equations to solve for x.
Using Equation 1: 2x + 5(-2) = -4
2x - 10 = -4
2x = -4 + 10
2x = 6
x = 3
So, the solution to the system of equations is x = 3 and y = -2.