solve the system by the elimination method:
5x+3y=-13 & 7x-2y=11
Multiply equation 1 by 2 and multiply equation by 3, then add. That will eliminate y and you can solve for x.
To solve the system of equations using the elimination method, we need to manipulate the equations by multiplying them in such a way that the coefficients of either the x or y terms will cancel out when added or subtracted.
Step 1: Multiply both sides of Equation 1 by 2 and Equation 2 by 3 to make the coefficients of y equal and opposite:
Equation 1: 2(5x + 3y) = 2(-13)
10x + 6y = -26
Equation 2: 3(7x - 2y) = 3(11)
21x - 6y = 33
Step 2: Let's add the modified equations to eliminate the y terms:
(10x + 6y) + (21x - 6y) = -26 + 33
31x = 7
Step 3: Divide both sides of the equation by 31 to solve for x:
x = 7/31
Step 4: Substitute the value of x back into either Equation 1 or Equation 2:
Using Equation 1:
5x + 3y = -13
5(7/31) + 3y = -13
35/31 + 3y = -13
Step 5: Solve for y by isolating the y variable:
3y = -13 - 35/31
3y = (-403 - 35)/31
3y = -438/31
Step 6: Divide both sides of the equation by 3 to solve for y:
y = -438/31 / 3
y = -438/31 * 1/3
y = -146/31
Therefore, the solution to the given system of equations is:
x = 7/31
y = -146/31
To solve the system of equations using the elimination method, we want to eliminate one of the variables by adding or subtracting the equations.
Let's start by eliminating the variable "y". To do this, we need to multiply the first equation by 2 and the second equation by 3. This will ensure that the coefficients of "y" have the same absolute value, allowing us to cancel them out.
Multiplying the first equation by 2 gives us:
(2)(5x + 3y) = (2)(-13) -> 10x + 6y = -26
Multiplying the second equation by 3 gives us:
(3)(7x - 2y) = (3)(11) -> 21x - 6y = 33
Now, we can add the two equations together to eliminate the "y" variable:
(10x + 6y) + (21x - 6y) = (-26) + (33)
10x + 21x + 6y - 6y = -26 + 33
31x = 7
Dividing both sides of the equation by 31 gives us:
x = 7/31
Now that we have the value of "x", we can substitute it back into one of the original equations to find the value of "y". Let's use the first equation:
5(7/31) + 3y = -13
Simplify this equation:
35/31 + 3y = -13
Subtracting 35/31 from both sides:
3y = -13 - 35/31
3y = (-403 - 35)/31
3y = -438/31
Dividing both sides by 3 gives us:
y = -146/31
Therefore, the solution to the system is x = 7/31 and y = -146/31.