2x+y=12
2x−4y=12
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
2x+y=12,2x−4y=12
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
2x+y=12
Subtract y from both sides of the equation.
2x=−y+12
Divide both sides by 2.
x=
2
1
(−y+12)
Multiply
2
1
times −y+12.
x=−
2
1
y+6
Substitute −
2
y
+6 for x in the other equation, 2x−4y=12.
2(−
2
1
y+6)−4y=12
Multiply 2 times −
2
y
+6.
−y+12−4y=12
Add −y to −4y.
−5y+12=12
Subtract 12 from both sides of the equation.
−5y=0
Divide both sides by −5.
y=0
Substitute 0 for y in x=−
2
1
y+6. Because the resulting equation contains only one variable, you can solve for x directly.
x=6
The system is now solved.
x=6,y=0