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Solve the system of equations below.
x + y = 7
2x + 3y = 16
A. (5, 2)
B. (2, 5)
C. (3, 4)
D. (4, 3)

Sagot :

Corsaquix

Answer:

A. (5, 2)

Step-by-step explanation:

Given

[tex]\begin{cases}x+y=7,\\2x+3y=16\end{cases}[/tex],

Multiply the first equation by 2, then subtract both equations to get rid of any terms with [tex]x[/tex]:

[tex]\begin{cases}2(x+y)=2(7),\\2x+3y=16\end{cases}\\\implies 2x+2y=14,\\2x+3y=16,\\2x-2x+2y-3y=14-16,\\-y=-2,\\y=\boxed{2}[/tex]

Substitute [tex]y=2[/tex] into any equation to solve for [tex]x[/tex]:

[tex]x+y=7,\\x+2=7,\\x=7-2=\boxed{5}[/tex]

Since coordinates are written as (x, y), the solution to this system of equations is (5, 2).

Answer:

A. ( 5 , 2 )

Step-by-step explanation:

solve by elimination method

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

  • x + y = 7, 2x + 3y = 16

To make x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 1.

  • 2x + 2y = 2 × 7, 2x + 3y = 16

Simplify.

  • 2x + 2y = 14, 2x+3y=16

Subtract 2x+3y=16 from 2x+2y=14 by subtracting like terms on each side of the equal sign.

  • 2x - 2x + 2y - 3y = 14 - 16

Add 2x to -2x. Terms 2x and -2x cancel out, leaving an equation with only one variable that can be solved.

  • 2y - 3y = 14 - 16

Add 2y to -3y.

  • -y = 14 - 16

Add 14 to -16.

  • -y = -2

Divide both sides by -1.

  • y = 2

Substitute 2 for y in 2x+3y=16. Because the resulting equation contains only one variable, you can solve for x directly.

  • 2x + 3 × 2 = 16

Multiply 3 and 2

  • 2x + 6 = 16

Subtract 6 from both sides of the equation.

  • 2x = 10

Divide both sides by 2.

  • x = 10

The system is now solved.

x = 5 and y = 2

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