In some linear systems, neither variable can be eliminated by adding or subtracting the equations directly. In systems like these, we need to multiply one of the equations by a constant so that adding or subtracting the equations will eliminate one variable.
The following steps will be useful to solve a system of equation using multiplication and subtraction.
Step 1 :
Decide which variable to be eliminated.
Step 2 :
Multiply one equation by a constant to make the coefficient same for the variable which has to be eliminated.
Step 3 :
After having multiplied one equation by constant, add or subtract to eliminate that variable and solve for the other variable.
Step 4 :
Substitute the value of the variable received in step 3 into one of the equations to find the value of the eliminated variable.
Question :
Solve the system of equations by multiplying and adding.
3x + 5y = 11
2x + 15y = 19
Answer :
Step 1 :
Let us eliminate the variable y in the given two equations.
3x + 5y = 11 -----(1)
2x + 15y = 19 -----(2)
Step 2 :
To make the coefficient of y same in both the equations, multiply the first equation by 3.
(1) ⋅ 3 -----> 9x + 15y = 33 -----(3)
In equations (2) and (3), the variable y is having the same coefficient, and also having the same sign.
Step 3 :
Subtract equation (2) from (3) to eliminate the variable y.
(3) - (2) ----> (9x + 15y) - (2x + 15y) = 33 - 19
9x + 15y - 2x - 15y = 33 - 19
Simplify.
7x = 14
Divide both sides by 7.
7x / 7 = 14 / 7
x = 2
Step 4 :
Substitute the value of x into one of the equations to find the value of y.
3x + 5y = 11
3(2) + 5y = 11
6 + 5y = 11
Subtract 6 to both sides.
(6 + 5y) - 6 = (11) - 6
6 + 5y - 6 = 11 - 6
Simplify.
5y = 5
Divide both sides by 5
5y / 5 = 5 / 5
y = 1
So, the solution to the system is
(x, y) = (2, 1)
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Nov 21, 22 10:22 AM
Nov 21, 22 10:20 AM
Nov 21, 22 06:42 AM