8.1. Systems of Two Equations and Two Unknowns http://www.ck12.org
- Solve the following system using elimination:
5 x−y= 22
− 2 x+ 7 y= 19- Solve the following system using elimination:
11 ·^1 x− 5 ·^1 y=− 38
9 ·^1 x+ 2 ·^1 y=− 25Answers:
- Start by scaling both of the equations by^12. Then notice that you have 3yand− 7 y. Rescale the first equation by
7 and the second equation by 3 to make the coefficients ofyat 21 and -21. There are a number of possible ways to
eliminatey.
70 x+ 21 y=− 112
27 x− 21 y= 15Add, solve forx=−1, substitute and solve fory.
Final Answer: (-1, -2)
- Start by scaling the first equation by 7 and notice that theycoefficient will immediately be eliminated when the
equations are summed.
35 x− 7 y= 154
− 2 x+ 7 y= 19Add, solve forx=^17333. Instead of substituting, practice eliminatingxby scaling the first equation by 2 and the
second equation by 5.
10 x− 2 y= 44
− 10 x+ 35 y= 95Add, solve fory.
Final Answer:(^17333 ,^13933 )
- To eliminate^1 y, scale the first equation by 2 and the second equation by 5.
To eliminate^1 x, scale the first equation by -9 and the second equation by 11.
Final Answer:(−^13 , 1 )