Question

2. Use the linear combination method to solve the system of equations 2x-3y=13, x+2y=-4. Explain each step of your solution.

Answer 1

2x-3y=13

x+2y=4

1) solve for x or y in one of the equations

the second equation makes this super easy: x=4-2y

2) perform a substitution by inserting the value of x into the first equation

2(4-2y)-3y=13

3) solve for y

8-4y-3y=13 --> 8-7y=13 --> -7y=5 --> y = -5/7

4) replace your y value in any of the equations to solve for x; I prefer to use the equation already set to x (x=4-2y)

x=4-2(-5/7) --> x= 38/7 OR 5+3/7

HOPE THIS HELPS!!!

Answer 2

y = -3 and x = 2

Step-by-step explanation:

Given:

• 2x -3y = 13
• x + 2y = -4

make the x coefficients similar:

( 2x -3y = 13 ) * 1 → 2x -3y = 13

( x + 2y = -4 ) * 2 → 2x + 4y = -8

solve using combination method:

2x - 3y = 13

- 2x - 4y = +8

----------------------

0x - 7y = 21

-7y = 21

y = -3

Find x:

x + 2y = -4

x + 2y = -4

x = -4 - 2(-3)

x = -4 +6

x = 2