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:( , )

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 )

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KarpaT KarpaT · Answer 2 · 2022-07-19T14:09:24+02:00

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,

[tex]x + 3y = 7[/tex]

⇒ [tex]x=7-3y[/tex]

Substitute x in equation 2, we get

[tex]2x + 4y = 8[/tex]

⇒ [tex]2(7-3y) + 4y = 8[/tex]

⇒ [tex]14-6y+4y=8[/tex]

⇒ [tex]14-8=2y[/tex]

⇒ [tex]6=2y[/tex]

⇒ [tex]y=\frac{6}{2}[/tex]

⇒ [tex]y=3[/tex]

Thus, [tex]x=7-3(3)[/tex]

⇒ [tex]x=7-9[/tex]

⇒ [tex]x=-2[/tex]

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

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