Using the Substitution Method, solve the system x - 3y = 102x + 4y = -10?

Hi,

x - 3y = 10
2x + 4y = -10

Solve the first equation for x:
x = 3y + 10

Substitute this into the second expression in place of x and solve.
2x + 4y = -10

2(3y + 10) + 4y = -10

6y + 20 + 4y = -10

10y + 20 = -10

10y = -30

y = -3

If y = -3 and x = 3y + 10, then x = 1.

(1,-3) <==ANSWER

I hope that helps!! :-)

Solving for y:
x - 3y = 102x + 4y
7y = - 101x
y = - 101x/7

102x + 4y = - 10
51x + 2y = - 5
2y = (- 5 - 51x)
y = (- 5 - 51x)/2

Value of x:
2(- 101x) = 7(- 5 - 51x)
- 202x = - 35 - 357x
155x = - 35
31x = - 7
x = - 7/31

Value of y:
= (- 101[- 7/31])/7
= - 101(- 1/31)
= 101/31 or 3 8/31

Answer: x = - 7/31, y = 101/31 or 3 8/31

Proof:
- 7/31 - 3(101/31) = 102(- 7/31) + 4(101/31) = - 10
- 7/31 - 303/31 = - 714/31 + 404/31 = - 10
- 310/31 = - 310/31 = - 10
- 10 = - 10 = - 10

Presentation not good !

x - 3y = 10
2x + 4y = - 10

- 2x + 6y = - 20
2x + 4y = - 10--------ADD

10y = - 30
y = - 3

x + 9 = 10
x = 1

x = 1 , y = - 3

x - 3y = 10
2x + 4y = -10

x - 3y = 10
x = 3y + 10

2x + 4y = -10
2(3y + 10) + 4y = -10
6y + 20 + 4y = -10
6y + 4y = -10 - 20
10y = -30
y = -30/10
y = -3

x - 3y = 10
x - 3(-3) = 10
x - (-9) = 10
x + 9 = 10
x = 10 - 9
x = 1

∴ x = 1 , y = -3

x - 3y = 10 .......................... can be written as: x = 10 + 3y
2x + 4y = -10

2(10 + 3y) + 4y = -10 ........ substitute (10 + 3y) for x
10y = -30
y = -3
x = 10 + 3(-3)
x = 1

Answer: x = 1 and y = -3

x - 3y = 102x + 4y = -10 substituting x = 3y + 10 from first into second equation 2(3y+10) + 4y = -- 10 OR y = -- 3 and x = 3(--3)+10 = 1
x = 1, y = --3