solve by the elimination method
x + y = -2
4x - 6y = -3
first one times 6
6x + 6y = -12
4x - 6y = -3
add them
10x = -15
x = -15/10 = -3/2
sub into the 1st
-3/2 + y = -2
y = 3/2 - 2 = -1/2
x = -3/2 , y = -1/2
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply the first equation by 2 to make the coefficients of x in both equations the same:
2(x + y) = 2(-2)
This simplifies to:
2x + 2y = -4
Step 2: Rewrite the second equation:
4x - 6y = -3
Step 3: Add the two equations together to eliminate the x variable:
2x + 2y = -4
+ 4x - 6y = -3
------------------
6x - 4y = -7
Step 4: Multiply both sides of the equation by -1 to simplify the equation:
-1(6x - 4y) = -1(-7)
This gives us:
-6x + 4y = 7
Step 5: Add the equation obtained in step 4 to the second equation:
-6x + 4y = 7
+ 4x - 6y = -3
-----------------
-2x - 2y = 4
Step 6: Divide the equation obtained in step 5 by -2 to isolate y:
(-2x - 2y)/-2 = 4/-2
This simplifies to:
x + y = -2
Step 7: Add the equation obtained in step 6 to the first equation:
x + y = -2
+ x + y = -2
--------------
2x + 2y = -4
Step 8: Simplify the equation:
2x + 2y = -4
Divide both sides of the equation by 2:
(x + y)/2 = -4/2
This gives us:
x + y = -2
Step 9: Notice that the equation obtained in step 6 and step 7 are the same. This means that the system of equations is dependent, and the solution is infinite. Any pair of values for x and y that satisfy the equation x + y = -2 will be a solution to the system.
Therefore, the solution to the system of equations is x + y = -2.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant to make the coefficients of one variable the same (or additive inverses).
Let's start by multiplying equation (1) by 4 in order to make the coefficients of x the same in both equations:
4(x + y) = 4(-2) (multiply equation (1) by 4)
4x + 4y = -8
Now we have the following system of equations:
4x + 4y = -8 (equation 1, after multiplying by 4)
4x - 6y = -3 (equation 2)
Step 2: Add or subtract the two equations to eliminate one variable.
Now, subtract equation (2) from equation (1) to eliminate x:
(4x + 4y) - (4x - 6y) = -8 - (-3)
4x + 4y - 4x + 6y = -8 + 3
10y = -5
Simplifying further, we have:
10y = -5
Step 3: Solve for the remaining variable.
To find the value of y, divide both sides of the equation by 10:
10y/10 = -5/10
y = -1/2
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's substitute y = -1/2 into equation (1):
x + (-1/2) = -2
x - 1/2 = -2
To isolate x, add 1/2 to both sides of the equation:
x - 1/2 + 1/2 = -2 + 1/2
x = -2 + 1/2
x = -3/2
So the solution to the system of equations is x = -3/2 and y = -1/2.
Therefore, the solution is (x, y) = (-3/2, -1/2).