Solving a System of Two Linear Equations with Substitution

coefficients of the first equation

a

4

b

4

c

3

coefficients of the second equation

d

6

e

3

f

2

show steps

1

2

3

4

5

1. Rearrange the first equation.

2. Solve that equation for x.

3. Substitute for x in the second equation.

4. Solve that equation for y.

5. Substitute for y in step 2.

Solve the system of the equations:

4x+4y3

6x+3y2

4x3-4y

x

3

4

-y

6

3

4

-y+3y2

y

5

6

x-

1

12

This Demonstration solves a system of two linear equations with substitution. It solves the first equation for

x

and then substitutes

x

into the second equation. A new equation is then solved for

y

. Two equivalent equations give the identity, so there are infinitely many solutions; in case of a contradictory (inconsistent) system, there are no solutions.