Simultaneous Equations
2x+y = 7 and x - y = 2
Compare the two equations. What can we do to eliminate one of the variables?
Think about zero pairs.
Add the equations
2x + y = 7
x - y = 2
3x = 9
x = 3
Substitute x into 2x + y = 7
2(3) + y = 7
6 + y = 7
y = 1
2x + y = 5 and x + y = 1
Compare the two equations. What can we do to eliminate one of the variables?
Flip the second equation and compare the equations again.
Add the equations
2x + y = 5
-x - y = -1
x = 4
Substitute x into 2x + y = 5
2(4) + y = 5
8 + y = 5
y = -3
Solve 2x + y = 1 and x + y = -2
Compare the two equations. What can we do to eliminate one of the variables?
Flip the second equation and compare the equations again.
Add the equations
2x + y = 1
-x - y = 2
x = 3
Substitute x into 2x + y = 1
2(3) + y = 1
6 + y = 1
y = -5
Solve 2x – y = 1 and x – y = -2
Compare the two equations. What can we do to eliminate one of the variables?
Flip the second equation
Add the equations
2x - y = 1
-x + y = 2
x = 3
Substitute x into 2x - y = 1
2(3) - y = 1
6 - y = 1
y = 5