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Chapter 5: Q. 351 (page 679)

Solve a System of Equations by Elimination

In the following exercises, solve the systems of equations by elimination.

x+y=12x鈭�y=鈭�10

Short Answer

Expert verified

The solution is (1,11)

Step by step solution

01

Step.1 Given information 

Here two equations x+y=12x-y=-10are given.

We have to find the solution to these equations

02

Step 2. Description of finding a solution for given equations

From both equations, we can understand that the equations are in standard form and coefficients of y are opposite. To eliminate y we can add both equations and will get resultant equation containing 1 variable, x+y=121x-y=-102Add1+22x=2鈬�x=1Togetvalueforthevariableywehavetosustitutex=1in(1)or(2)Soputx=1in(1)weget1+y=12y=12-1=11Nowthesolutionforxandyare(1,11)

03

Step 3. Checking  the (1,11) is the solution for the original equations 

The solution for the given equation is (1,11). now put x=1 y=11 in both original equations

x+y=12,Putx=1,y=11inthisorginalequationweget1+11=1212=12,x-y=-10substituethevaluesx=1andy=11then1-11=1-10-10=-10Bothequationsatisfyingthesolution.Soorderedpair(1,11)isasolutionforgivenequations.

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