How do you solve 3x+y=5 and x-2y=11 using substitution?

2 Answers
Jan 18, 2017

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for y:

3x - color(red)(3x) + y = 5 - color(red)(3x)

0 + y = 5 - 3x

y = 5 - 3x

Step 2) Substitute color(red)(5 - 3x) for y in the second equation and solve for x:

x - 2(color(red)(5 - 3x))= 11

x - (2 xx color(red)(5)) + (2 xx color(red)(3x))= 11

x - 10 + 6x = 11

7x - 10 = 11

7x - 10 + color(red)(10) = 11 + color(red)(10)

7x - 0 = 21

7x = 21

(7x)/color(red)(7) = 21/color(red)(7)

(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 3

x = 3

Step 3) Substitute color(red)(3) for x in the solution to the first equation at the end of Step 1

y = 5 - (3 xx color(red)(3))

y = 5 - 9

y = -4

The solution is x = 3 and y = -4

Jan 18, 2017

x = -1/7, y=-39/7. Explanation below.

Explanation:

Using the second equation, we can express y in terms of x as such:

-2y = 11 - x => y = -11/2+x/2.

Substituting this y value in the first equation:

3x + (-11/2 + x/2) = 5 => (7x)/2 = -1/2 =>

=>7x = -1 => x = -1/7.

Now, we can substitute this x value in the second equation to find y (any equation will do, but x is easier to evaluate than 3x)

-1/7 - 2y = 11 => 2y = -78/7 => y = -78/14 = -39/7