how to do this math equation ? please explain?

Question

x+3y=34

5x-y=10

i will be asking more math qustions later

Answer 1

ok i help you:

solution:

we can solve this by elimination method or sustitution method.

i used the substitution method.


x+3y=34 (eq1)

5x-y=10 (eq2)

from eq 1,

x = 34 -3y (eq3)

now we substitute the eq 3 to eq 2 for value of x,

5x-y=10

5 (34 -3y) - y=10

simplify it,

170 - 15y - y = 10

solve for y,

170 -10 = 15y + y

160 = 16 y

10 = y
is the answer,

now substitute the value of y in eq 3 or eq 1 to get the value of x,

i used eq 3,

x = 34 -3y (eq3) since y = 10

now we have,

x = 34 - 3 (10)

x = 34 -30

x = 4 is the answer.

to check your answer substitute the value of x and y in any of the eq 1 or eq 2, and must satisfy the equation

good luck!!

Answer 2

Solve for x in terms of y, and then plug that value in the 2nd equation.
So if x+3y=34, then x=34-3y

Substituting 34-3y for x, If 5x-y=10, then 5(34-3y)-y=10
It's all down hill from here
Multiply out: 170-15y-y=10
160=16y
y=10

Solving for x:
x+3y=34
x+3(10)=34
x+30=34
x=4

Answer 3

There are four ways to solve a system of linear equations:
1. Elimination
2. Substitution
3. Graphically
4. Using determinants

I used the elimination method
5x-y=10 so by multiplying we have 15x-3y=30 (1)
x+3y=34 (2)

By adding (1) and (2) we take:
(1) + (2): 15x - 3y +x + 3y = 30 + 34
16x=64
x= 4

By putting the value 4 to x in (2) we take:
x+3y=34
4+3y=34
3y=34-4
3y=30
y=10

So (x,y)=(4,10)

Answer 4

x + 3y = 34
x = 34 - 3y ------- i

5x - y = 10 -------- ii

we use the subsitution method... subsitute equation i into equation ii
5(34 - 3y) - y = 10
170 - 15y - y = 10
170 - 16y = 10
16y = 170 - 10
16y = 160
y = 160/16
y = 10

x = 34 - 3y
x = 34 - 3(10)
x = 34 - 30
x = 4

therefore,
x = 4
y = 10