-4x + 7y = -3
-4x – 3y = 7
solve using elimination
x = 7y/4 + 3/4
y = 4x/7 + 3/7
x = -3y/4 - 7/4
y = -4x/3 - 7/3
just subtract them:
10y = -10
y = -1
plug that into the first:
-4x + 7(-1) = -3
-4x = -3+7 = 4
x = -1
x = -1, and y = -1
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the two equations together. Here's how to do it step by step:
1. Start by writing down the two equations:
-4x + 7y = -3 (Equation 1)
-4x - 3y = 7 (Equation 2)
2. In this case, we can eliminate the variable "x" by subtracting Equation 2 from Equation 1. This will eliminate the "-4x" terms:
(-4x + 7y) - (-4x - 3y) = (-3) - (7)
Simplifying the equation:
-4x + 7y + 4x + 3y = -3 - 7
Combine like terms:
7y + 3y = -10
Simplify further:
10y = -10
3. Now we have a simplified equation with only one variable, "y." To find the value of "y," divide both sides of the equation by 10:
10y/10 = -10/10
As a result, we get:
y = -1
4. We have found the value of "y." Now, substitute this value back into either of the original equations to find the value of "x." Let's use Equation 1:
-4x + 7(-1) = -3
Simplify the equation:
-4x - 7 = -3
Add 7 to both sides of the equation to isolate "-4x":
-4x = -3 + 7
Simplify further:
-4x = 4
5. Divide both sides of the equation by -4 to solve for "x":
-4x/-4 = 4/-4
Thus, we get:
x = -1
6. Therefore, the solution to the given system of equations is x = -1 and y = -1.
To verify the solution, substitute the values of x and y back into both equations and see if they satisfy both equations.