Question

In two or more complete sentences, describe how the substitution method works for solving a two-order system of equations.

Answer 1

The first step is to set one equation equal to x or equal to y.
Ex. y = ..... or x = .....
The next step is to substitute that equation into the second equation in place of the x (or y), whichever you set it equal to.

Ex. x + y = 3
2x + y = -1

y = -x + 3 2x + (-x + 3) = -1
x + 3 = -1
x = -4
y = -(-4) + 3 y = 7 (-4,7)

Answer 2

The first step is to set one of the equation equal to x or y. Then substitute this value into the other equation to find the value of the other variable. Finally, put the value obtained into the relation taken at the start.

Explanation:

Let us consider an example,

3x + y = 8

x + y = 6.

The first step is to set one of the equation equal to x or y.

i.e. x = 6 - y.

Next step is to substitute this value into the other equation.

i.e. 3×(6-y) + y = 8

i.e. 18 - 3y + y = 8

i.e. -2y = -10

i.e. y = 5.

Finally, we put this value of y into the relation taken at the start

i.e. x = 6 - y

i.e. x = 6 - 10

i.e x = 4.

Hence, the solution of this system of equations using substitution method is (x, y) = ( 4, 5).