Substitution The idea here is to solve one of the equations

Substitution The idea here is to solve one of the equations for one of the variables and substitute it into the other. For example, we could write the first equation as 3 y = -2x + 4(mod1 7) then multiply both sides by the multiplicative inverse of 3, which is 6, to get y = -12x + 24 = 5x + 7(mod1 7) Substituting that into the second equation gives 5x + 4(5x + 7) = 2(mod1 7) which simplifies to 8x = 8(mod1 7) or x = 1(mod1 7) We now substitute that back into the equation y = 5x + 7(mod1 7) to find that y = 12(mod1 7) Use substitution to solve the same system by solving the first equation for x instead of for y.

Solution

we Have y=5x+7 and 3y=-2x+4

we can write 3y=-2x+4 as x=-3/2y+2

By substitution method we get

y=5(-3/2y+2)+7

y=-15/2y+10+7

y=-15/2y+17

17/2y=17

y=2

Substitute y=2 in y=5x+7

2=5x+7

5x=-5

x=-1