Question

Use the substitution method to solve the system of equations. Choose the

correct ordered pair,
2y + 5x = 13
2y - 3x = 5
O
A (1,4)
B. (-3, 14)
O
O c. (3,7)
O D. (-1,9)

Answer 1

A. (x , y) = ( 1, 4) is the SOLUTION of the given system of equations.

Explanation:

Here, the given set of equations is:

2 y + 5x = 13 ....... (1)

2y - 3x = 5 ...... (2)

Now, to solve this question by SUBSTITUTION:

From (1), we get:

2 y + 5x = 13 ⇒ 2 y = 13 - 5 x

or,
`y = (13 - 5x)/(2)`

Put this value of y in (2) . We get

`2y - 3x = 5  \implies 2*((13-5x))/(2)  - 3x = 5\\\implies 13 - 5 x - 3x = 5\\\implies- 8x  = -8\\\implies x = 1`

Now, x = 1, put this value of x in (1),

2 y + 5x = 13 ⇒ 2y + 5(1) = 13

or, 2 y = 13- 5 = 8

or, y = 8 / 2 = 4, ⇒ y = 4

Hence, x = 1, y = 4 is the SOLUTION of the given system of equations.