2x plus y equals 5 2y plus x equals 4?

Answer 1

one solution

write down the 2 equations

eq 1: 2x + y = 5

eq 2: 2y + x = 4

get a value for x from eq 2

x = 4 - 2y

substitute 4 - 2y for x in eq 1

2(4 - 2y) + y = 5

8 - 4y +y = 5

-3y = -3

y=1

substitute 1 for y in eq 2

2(1) + x = 4

2 + x = 4

x = 4-2

x = 2

Answer 2

2x + y = 5

2y + x = 4

This is SIMULTANEOUS Equations.

To solve , arbitrarily select a letter to eliminate, In this case 'x'

To do this the coefficients of 'x' must be the same , but of opposite sign. Hence multiply the bottom equation by '-2'

Hence

2x + y = 5

-2x - 4y = =8

Add

-3y = -3

Divide both sides by '-1'

3y = 3

y = 1

When y= 1

Substitute back in to either eq'n

2x + 1 = 5

Subtract '1' from both sides

2x = 4

x = 2

Hence the answer is ( x,y) = ( 2,1)