There are 2 ways to do each of them.
For the 1st one lets start with substitution.
2x+y=10
x-y=2
SUBSTITUTION
Step: Solve2x+y=10for y:
2x+y=10
2x+y+−2x=10+−2x(Add -2x to both sides)
y=−2x+10
Step: Substitute−2x+10foryinx−y=2:
x−y=2
x−(−2x+10)=2
3x−10=2(Simplify both sides of the equation)
3x−10+10=2+10(Add 10 to both sides)
3x=12
3x
3
=
12
3
(Divide both sides by 3)
x=4
Step: Substitute4forx in y=−2x+10:
y=−2x+10
y=(−2)(4)+10
y=2(Simplify both sides of the equation)
Answer:
x=4 and y=2
Now let's do Elimination
ELIMINATION
2x+y=10
x−y=2
Add these equations to eliminate y:
3x=12
Then solve3x=12for x:
3x=12
3x
3
=
12
3
(Divide both sides by 3)
x=4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
2x+y=10
Substitute4forxin2x+y=10:
(2)(4)+y=10
y+8=10(Simplify both sides of the equation)
y+8+−8=10+−8(Add -8 to both sides)
y=2
NUMBER 2
Substitution
18x−y+18=21;x−y=−48
Step: Solve18x−y+18=21for y:
18x−y+18+−18=21+−18(Add -18 to both sides)
18x−y=3
18x−y+−18x=3+−18x(Add -18x to both sides)
−y=−18x+3
−y
−1
=
−18x+3
−1
(Divide both sides by -1)
y=18x−3
Step: Substitute18x−3foryinx−y=−48:
x−y=−48
x−(18x−3)=−48
−17x+3=−48(Simplify both sides of the equation)
−17x+3+−3=−48+−3(Add -3 to both sides)
−17x=−51
−17x
−17
=
−51
−17
(Divide both sides by -17)
x=3
Step: Substitute3forxiny=18x−3:
y=18x−3
y=(18)(3)−3
y=51(Simplify both sides of the equation)
Elimination
Multiply the second equation by -1, then add the equations together.
(18x−y+18=21)
−1(x−y=−48)
Becomes:
18x−y+18=21
−x+y=48
Add these equations to eliminate y:
17x+18=69
Then solve17x+18=69for x:
17x+18+−18=69+−18(Add -18 to both sides)
17x=51
17x
17
=
51
17
(Divide both sides by 17)
x=3
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
18x−y+18=21
Substitute3forxin18x−y+18=21:
(18)(3)−y+18=21
−y+72=21(Simplify both sides of the equation)
−y+72+−72=21+−72(Add -72 to both sides)
−y=−51
−y
−1
=
−51
−1
(Divide both sides by -1)
y=51
SVS
