0

# How do I solve this using substitution

-4x+3y=-24
-5x+y=-19

### 3 Answers by Expert Tutors

Michael V. | Great Tutor in Multiple SubjectsGreat Tutor in Multiple Subjects
1
Solve using substitution
-4x + 3y = -24
-5x + y = -19
• Start by rearranging one of the equations in terms of a variable
• Lets choose the bottom equation and solve for y
-5x + y = -19
• Add 5x to both sides
-5x + y + 5x = -19 + 5x
y = 5x - 19
• Now replace y in the top equation with 5x - 19
-4x + 3y = -24
-4x + 3(5x - 19) = -24
• Distribute the 3 across the parentheses
-4x + 15x - 57 = -24
• Combine like terms then add 57 to both sides
11x - 57 = -24
11x - 57 + 57 = -24 + 57
11x = 33
• Now divide both sides by 11
11x/11 = 33/11
x = 3
• Finally, we can substitute our value for x in the bottom equation
y = 5x - 19
y = 5(3) - 19
y = 15 - 19
y = -4

x = 3, y = -4
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
-4X + 3Y = -24
-5x  + Y = -19

Let's solve for Y in terms of X from the 2nd equation:

Y = 5x -19

Plug in the Y in 1st equation:

- 4X + 3( 5X - 19) = -24

-4X + 15X - 57 = -24

11 X = 57 -24 = 33    X = 3

Plug in X into 1st equation:
-4(3) +3Y = -24
3Y = -24 + 12 = -12      Y = -12 /3 = -4        Y= -4

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
0
Hi Lindsay;
-4x+3y=-24
-5x+y=-19
Let's isolate one variable.
The second equation is easier.
-5x+y=-19
Let's add 5x to both sides...
5x-5x+y=5x-19
y=5x-19
Let's plug this into the first equation...
-4x+3y=-24
-4x+[(3)(5x-19)]=-24
Let's distribute the 3 within the brackets...
-4x+(15x-57)=-24
-4x+15x-57=-24
Let's combine like terms...
11x-57=-24
Let's add 57 to both sides...
57+11x-57=-24+57
11x=33
Let's divide both sides by 11...
(11x)/11=33/11
x=3
Let's plug this into either equation to establish y.  I randomly select the first...
-4x+3y=-24
[(-4)(3)]+3y=-24
-12+3y=-24
3y=-12
y=-4
Let's plug both values into the second equation to verify...
-5x+y=-19
[(-5)(3)]+(-4)=-19
-15-4=-19
-19=-19
It works!