Systems of Equations

3x - 4y = -15
5x + y = -2

Please show steps so I can understand how to do this. Answer book says (-1,3)

3x-4y=-15
5x+y=-2
---- y=-2-5x (plug this into first equation inplace of "y")
----------3x-(4(-2-5x))=-15
----------3x+8+20x=-15 multiply what in ( ) by the -4
----------23x+8=-15 combine the "x" values
----------23x=-23 subtract the 8 over
---------- x= -1 divide by 23

Now plug the -1 in either equation to answer for "y"
5(-1) + y = -2
-5+y=-2
y=3

I would start with the second equation, because it is easier to work with

5x + y = -2
solve for y by subtracting 5x from both sides

5x + y - 5x = -2 - 5x
y = -2 - 5x (use this equation at the end to solve for the value of y)

now that you have an equation for "y", substitute it into the first equation

3x - 4y = -15
3x -4(-2 -5x) = -15

now expand the "-4" into the parentheses being mindful of multiplying by a negative number

3x + 8 + 20x = -15
combine the like terms

23x + 8 = -15
subtract 8 from both sides of the equation

23x + 8 - 8 = -15 - 8
23x = -23
divide both sides of the equation by 23

23x/23 = -23/23
x = - 1 <====

substitute x = -1 into the equation from above y = -2 - 5x to solve for y
y = -2 -5(-1)
y = -2 + 5
y = 3 <====

the answer is (-1, 3) <====

take 5x+y=-2
subtract 5x from each side
y=-5x-2
Plug the above equation into the first equation
3x-4y=-15
3x-4(-5x-2)=-15
Distribute
3x+20x+8=-15
Collect like terms
23x+8=-15
Subtract 8 to from side
23x=-23
Divide each side by 23
x=-1
Plug the value for x into the second equation
5x+y=-2
5(-1)+y=-2
Multiply
-5+y=-2
Add 5 to each side
y=3
Answer (-1,3)

You must elininate one variable to start with.

we will eliminate y
multiply 5x + y = -2 by 4

20x + 4y = -8

Add the two equations

23x = -23

so x = -1

Substitute for x in either equation to get y

3(-1) -4y = -15

-4y = -12

so y = + 3

(5x+y=-2)4
20x+4y=-8

3x-4y=-15
20x+4y=-8

23x=-23
x=-1
Then, plug in -1 for x in either of the equations and it's solved!