8.1. Systems of Two Equations and Two Unknowns http://www.ck12.org
You can substitutexinto the first equation to solve fory.
6 ·^53 − 7 y= 8
10 − 7 y= 8
− 7 y=− 2
y=^27The point(^53 ,^27 )is where these two lines intersect.
Example C
Solve the following system of equations:
5 ·^1 x+ 2 ·^1 y= 11
1
x+1
y=^4Solution: The strategy of elimination still applies. You can eliminate the^1 yterm if the second equation is scaled by
a factor of -2.
5 ·^1 x+ 2 ·^1 y= 11
− 2 ·^1 x− 2 ·^1 y=− 8Add the equations together and solve forx.
− 3 ·^1 x+ 0 ·^1 y= 3
− 3 ·^1 x= 3
1
x=−^1
x=− 1Substitute into the second equation and solve fory.
1
− 1 +1
y=^4
− 1 +^1 y= 4
1
y=^5
y=^15