Solve for x and y x 2y 10 x y 4 Solve for x and y 2x 3y

Solve for x and y: x + 2y = 10 x - y =4 Solve for x and y: 2x + 3y = 4 x - y = 2 Solve the following systems y = 3x + 10 y = -2x + 5

solution 1:

we are given two equations

x+2y=10 and x-y=4. we need to solve for x and y.

let us consider the equation x-y=4

=> y=x-4 now let us substitute this y in x+2y=10

=> x+2(x-4)=10

=> x+2x-8=10

=> 3x-8=10

=> 3x=18 => x=6 substituting x in y=x-4 gives us y=6-4 = 2

therefore x=6 and y=2. this method is called method of substitution.

we can always check our answers by substituting them back into the equations. like x+2y=10 6+2x2=10 so the answer we got are correct.

solution 2:

this problem can also be solve by the above method but let us see another method , method of elimination

given equations are 2x+3y=4 and x-y=2. here we aim to eliminate y by multiplying the eqation x-y=2 by 3.

which gives us 3x-3y=6 and adding this to 2x+3y=4.

2x+3y+3x-3y=6+4

5x=10

x=2 substitute it in x-y=2

2-y=2 imples y=0.

therefore x=2, y=0

solution 3:

y=3x+10 => y-3x=10

y=-2x+5 => y+2x=5

now substract y-3x=10 from y+2x=5

y+2x-(y-3x)=5-10

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

5x=-5 therefore x=-1 substitute it in y=3x+10

y=3(-1)+10

y=-3+10

y=7

therefore x=-1 and y=7