Question

Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.

1. Isolate x in the first equation: x = 7 − 3y2. 

Substitute the value for x into the second equation: 2(7 − 3y) + 4y = 83.

 Solve for y: 14 − 6y + 4y = 814 − 2y = 8−2y = −6y = 34. 

Substitute y into either original equation:x =
7 − 3(3)5. 

Write the solution as an ordered pair:( , )

 

Answer 1

hello :
x + 3y = 7....(1)
2x + 4y = 8....(2)
by (1) : x= 7-3y
Substitute in (2) :   2(7-3y)+4y =8
14-6y +4y =8
-2y =-6
y =3
x =7-3(3)
x = -2
Write the solution as an ordered pair:(-2 ,3 )

Answer 2

The solution to the system of equations as an ordered pair is (-2,3).

What is a system of equation?

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

The system of equations,

x + 3y = 7 ------- (1) and

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

Now consider equation 1,

$x + 3y = 7$

⇒ $x=7-3y$

Substitute x in equation 2, we get

$2x + 4y = 8$

⇒ $2(7-3y) + 4y = 8$

⇒ $14-6y+4y=8$

⇒ $14-8=2y$

⇒ $6=2y$

⇒ $y=\frac{6}{2}$

⇒ $y=3$

Thus, $x=7-3(3)$

⇒ $x=7-9$

⇒ $x=-2$

Hence we can conclude that the solution to the system of equations as an ordered pair is (-2,3).

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