How to use substitution to solve the system?  x+3y=-7 2x+4y=-4

samhouston | Certified Educator

Solve the first equation for x.

x + 3y = -7

x = -7 - 3y

Now substitute (-7 - 3y) in for x in the second equation.

2x + 4y = -4

2(-7 - 3y) + 4y  = -4

Solve to find the value of y.

-14 - 6y + 4y = -4

-14 - 2y = -4

-2y = 10

y = -5

Finally, substitute -5 in for y in the original equation and solve for x.

x + 3y = -7

x + 3(-5) = -7

x + -15 = -7

x = 8

Solution:  (x = 8, y = -5)

You can check this solution by substituting these values in for x and y in the second equation.

2x + 4y = -4

2(8) + 4(-5) = -4

16 + -20 = -4

-4 = -4

You can also check this solution by graphing the two equations and finding their point of intersection.

Notice that the point of intersection is (8, -5).

giorgiana1976 | Student

Writting one variable with respect to the other will lead to an equation that contains only one variable.

We notice that it is more easier to substitute x, from the top equation.

x = -3y - 7

We'll substitute x by it's equivalent expression in the 2nd equation and we'll get an equation that contains a single variable instead of two:

2(-3y - 7) + 4y = -4

-6y - 14 + 4y = -4

-2y = 14 - 4

-2y = 10

y = 10/-2

y = -5

x = -3*(-5) - 7

x = 15 - 7

x = 8

The solution of the system is represented by the pair (8 ; -5).