# Problem 833

Solve the system of equation by elimination, if a solution exists.

5x – y = -2

x + 3y = 22

Solution:-

To solve a system of linear equation using the elimination method, multiply one or both equations

by a nonzero number that will make the coefficients of one of the variables in the equation equal, except perhaps for sign. Then add or subtract the equation to eliminate one of the variables and solve the new equation for the remaining variable.

First choose a variable to eliminate. Make the terms containing that variable opposite by multiplying one or both equations by appropriate values.

Notice that in this situation, adding the equation will not eliminate either variable. One way to eliminate x is to leave the first equation unchanged and multiply the second equation by -5.

Multiply the second equation by -5.

-5x – 5y = -110.

Now add the equation to eliminate the variable x.

5x – y  = -2

-5x – 5y = -110

——————————-

-16y = -112

Solve for the remaining variable y.

-16y = -112

y = 7

Finally, substitute 7 for in either of the original equation and solve for the value of x.

Substitute 7 for y in the first equation and solve for x.

5x – 7 = -2

5x  = 5

x = 1

Thus, the solution to the system of equation is x = 1 and y = 7.