http://www.ck12.org Chapter 8. Systems and Matrices
Equation 2: 3x− 2 y= 18
Strategically choose to eliminateyby scaling the second equation by 6 so that the coefficient ofywill match at 12
and -12.
5 x+ 12 y= 72
18 x− 12 y= 108Add the two equations:
23 x= 180
x=^18023The value forxcould be substituted into either of the original equations and the result could be solved fory; however,
since the value is a fraction it will be easier to repeat the elimination process in order to solve forx. This time you
will take the first two equations and eliminatexby making the coefficients ofxto be 15 and -15. Scale the first
equation by a factor of 3 and scale the second equation by a factor of -5.
Equation 1: 15x+ 36 y= 216
Equation 2:− 15 x+ 10 y=− 90
Adding the two equations:
0 x+ 46 y= 126
y=^12646 =^6323The point(^18023 ,^6323 )is where these two lines intersect.
Example B
Solve the following system of equations:
6 x− 7 y= 8
15 x− 14 y= 21Solution: Scaling the first equation by -2 will allow theyterm to be eliminated when the equations are summed.
− 12 x+ 14 y=− 16
15 x− 14 y= 21The sum is:
3 x= 5
x=^53