Solve the systems of equations by elimination
2x+5y = -20
7x + 5y = 5
To solve the system of equations by elimination, we need to eliminate one variable by adding or subtracting the two equations. Let's eliminate the variable "y" by subtracting the first equation from the second equation:
(7x + 5y) - (2x + 5y) = 5 - (-20)
This simplifies to:
7x + 5y - 2x - 5y = 5 + 20
Combine like terms:
5x = 25
Divide both sides by 5:
x = 5
Now, substitute this value of x back into one of the original equations to solve for y. Let's use the first equation:
2x + 5y = -20
2(5) + 5y = -20
10 + 5y = -20
Subtract 10 from both sides:
5y = -30
Divide both sides by 5:
y = -6
Therefore, the solution to the system of equations is x = 5 and y = -6.
To solve the system of equations by elimination, we need to eliminate one variable by either adding or subtracting the two equations. Here's how we do it:
Step 1: Multiply the first equation by 7 and the second equation by 2 to make the coefficients of y the same.
(7)(2x + 5y) = (7)(-20)
(2)(7x + 5y) = (2)(5)
This yields:
14x + 35y = -140
14x + 10y = 10
Step 2: Now, subtract the second equation from the first equation to eliminate the x variable:
(14x + 35y) - (14x + 10y) = -140 - 10
Simplifying, we get:
25y = -150
Step 3: Solve for y by dividing both sides of the equation by 25:
25y/25 = -150/25
y = -6
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 + 5(-6) = -20
2x - 30 = -20
Step 5: Solve for x by isolating it on one side of the equation:
2x = -20 + 30
2x = 10
x = 10/2
x = 5
Therefore, the solution to the system of equations is x = 5 and y = -6.
To solve the system of equations by elimination, we will eliminate one variable by adding or subtracting the equations in a way that cancels out one of the variables.
1. Let's start by multiplying the first equation by 7 and the second equation by 2, so that the coefficients of y in both equations will be the same:
Equation 1: 7(2x + 5y) = 7(-20) -> 14x + 35y = -140
Equation 2: 2(7x + 5y) = 2(5) -> 14x + 10y = 10
2. Now subtract Equation 2 from Equation 1. This will cancel out the x term:
(14x + 35y) - (14x + 10y) = -140 - 10
25y = -150
3. Divide both sides of the equation by 25:
y = -150 / 25
y = -6
4. Substitute the value of y = -6 back into one of the original equations. Let's use Equation 1:
2x + 5(-6) = -20
2x - 30 = -20
2x = -20 + 30
2x = 10
5. Divide both sides of the equation by 2:
x = 10 / 2
x = 5
6. So the solution to the system of equations is x = 5 and y = -6.