How do I "solve the system"?

Question

It says to solve the system.

x -3y = 19
4x -5y =41

I forgot what I'm supposed to do.

It says the answer is (4, -5) in the back of the sheet.

Answer 1

There are several ways to solve a system like this.

I'll explain it by using substitution:

Solve one of the equations for one of the variables. I'll solve the first equation for x:

x - 3y = 19
x = 19 + 3y

Now, use this result to make a substitution into the other equation:

4x - 5y = 41
4(19 + 3y) - 5y = 41

Solve for y:

4*19 + 4 * 3y -5y = 41
76 + 12y - 5y = 41
7y = 41 - 76
7y = -35
y = -5

Now, use this value of y in the equation we solved for x:

x = 19 + 3y
x = 19 + (3 * -5)
x = 19 + (-15)
x = 4

Now, do these values satisfy the original equations?

4 - 3(-5) = 19
4 + 15 = 19
19 = 19

4(4) - 5(-5) = 41
16 + 25 = 41
41 = 41

OK. It all checks out.

Answer 2

x - 3y = 19 -----(1)
4x - 5y = 41 ----(2)

(1) => x = 3y + 19
replace x in (2)
4( 3y + 19) - 5y = 41
12y + 76 - 5y = 41
7y = -76 + 41 = - 35
y = -5
x = -15 + 19 = 4

Answer 3

x - 3y = 19.....(1)
4x - 5y = 41.....(2)

Consider (1)
x - 3y = 19
x = 3y + 19.....(3)

Substitute (3) in (2)
4x - 5y = 41
4(3y + 19) - 5y = 41
12y + 76 - 5y = 41
7y = -35
y = -5.....(4)

Substitute (4) in (3)
x = 3y + 19
x = 19 - 15
x = 4

x = 4, y = -5 is the solution

Answer 4

okay you can either multiply the top equation by 4 or multiply the top by 5 and the bottom one by 3. But, i will do the first choice. so.. if you multiply 4 to all the terms in the first equation, you get 4x-12y=76. So, if you subtract both the equation simultaneously, you get -7x=35 and x= -5. Now you solve for y by pluggin in -5 to the x. I will use the first equation becuase it is a easier one to do. so you get -5-3y=19. you get -3y=24, therefore y= -8. So x= -5 and y= -8.

Answer 5

x -3y = 19 ---- equ 1
4x -5y =41 ---- equ 2

substitute the value of x from equ 1 in equ 2
=> x=19+3y
so, 4(19+3y)-5y=41
7y= -35
y=-5

Now substitute the value of y in equ 1

x-3(-5)=19
x=4

Answer:
x=4
Y= -5

Answer 6

4(x-3y=19)

=4x-12y=76
- (4x-5y=41)

-7y=35
y=-5
x=4