Question
3x – y =12
3x + 5y = -6
- 3, -3
- 4, -4
- 5, -5
- 1, 1
Hint:
The Linear Combination Method, aka The Addition Method , aka The Elimination Method. Add (or subtract) a multiple of one equation to (or from) the other equation, in such a way that either the x-terms or the y -terms cancel out. Then solve for x (or y, whichever's left) and substitute back to get the other coordinate.
The correct answer is: 3, -3
There are different methods for solving simultaneous linear Equations:
I. Elimination of a variable
II. Substitution
III. Cross-multiplication
IV. Evaluation of proportional value of variables
Here, we will be using Elimination of a variable method.
Here, we have 2 equations
3x – y =12 (1)
3x + 5y = -6 (2)
Substracting equation(1) from equation (2), we get:
3x – y = 12
-
3x + 5y = -6
___________
= -6y =18
y= -3
Substitute the value of y in equation (1), we get:
3x -(-3) = 12
x= 3
Thus, (x, y) = (3,-3)
Related Questions to study
-5x – 2y = 9
-2x + 3y = 15
-5x – 2y = 9
-2x + 3y = 15
4x – 5y = -5
4x – 4y = 0
4x – 5y = -5
4x – 4y = 0
4x – 4y = 4
x – 3y = 5
4x – 4y = 4
x – 3y = 5
x – 5y = 20
x – y = 4
x – 5y = 20
x – y = 4
-x – y = -5
-3x + 3y = -3
-x – y = -5
-3x + 3y = -3
3y = 15
-3x – 5y = -10
3y = 15
-3x – 5y = -10
-4x – 5y = -1
-2x – 5y = 7
-4x – 5y = -1
-2x – 5y = 7
-2x – 5y = 10
-x – y = -1
-2x – 5y = 10
-x – y = -1
-5x + y = -3
5x – 4y = 12
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
-5x + y = -3
5x – 4y = 12
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
4x - 4y = 16
2x + y = -1
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
4x - 4y = 16
2x + y = -1
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
2x + y = -5
-4x + y = -5
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
2x + y = -5
-4x + y = -5
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
3x + 4y = 2
-4x + 3y = -11
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
3x + 4y = 2
-4x + 3y = -11
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
-2x + y = 11
x = -3
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In substitution method value of one variable is substituted an equation in order to get the value of that variable. After finding the value of one variable we can put that value in one equation to find the value of another variable.
-2x + y = 11
x = -3
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In substitution method value of one variable is substituted an equation in order to get the value of that variable. After finding the value of one variable we can put that value in one equation to find the value of another variable.
-5x – 2y = 6
x + 4y = 6
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
-5x – 2y = 6
x + 4y = 6
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
x – 2y = -13
x + 4y = 11
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
x – 2y = -13
x + 4y = 11
We can solve the equation in two variable using elimination method, substitution method and cross multiplication method. In elimination method we can find the solution of the two variables by cancelling one variable by adding, multiplying or subtracting both the equations from which we will get the value of one variable. After getting the value of one variable we can put the value of that variable in equation and get the value of another variable.
