Solve by substitution or elimination

2x + y = 5

2x - y = 3

Equation system:

{2x+y = 5 (equation 1)

{2x-y = 3 (equation 2)

Subtract equation 1 from equation 2:

2x+y = 5 (equation 1)

-2y = - 2 (equation 2)

Divide equation 2 by - 2:

2x+y = 5 (equation 1)

y = 1 (equation 2)

Subtract equation 2 from equation 1:

2x = 4 (equation 1)

y = 1 (equation 2)

Divide equation 1 by 2:

x = 2 (equation 1)

y = 1 (equation 2)

Answer:

x = 2

y = 1

Elimination

add the 2 equations togethter

2x+2x+y-y=3+5

4x=8

divide 4

x=2

subisute

2 (2) - y=3

4-y=3

subtract 4

-y=-1

mulitply - 1

y=1

x=2

y=1

subsitute

2x-y=3

add y to both sdies

2x=3+y

subtract 3

2x-3=y

subsitute 2x-3 for y

2x+2x-3=5

4x-3=5

add 3

4x=8

divide 4

x=2

subsitute

2 (2) - y=3

4-y=3

subtract 4

-y=-1

multpply - 1

y=1

x=2

y=1