Question

The system of equations can be solved using linear combination to eliminate one of the variables.

2x − y = −4 → 10x − 5y = −20
3x + 5y = 59 → 3x + 5y = 59
13x = 39
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

2x – y = –4
10x – 5y = –20
7x = 39
13x = 39

Answer 1

Answer:

888864578865434567899

Answer 2

SOLUTION

GIVEN

The system of equations can be solved using linear combination to eliminate one of the variables.

2x − y = −4 → 10x − 5y = −20

3x + 5y = 59 → 3x + 5y = 59

13x = 39

TO CHOOSE THE CORRECT OPTION

The equation which can replace 3x + 5y = 59 in the original system and still produce the same solution

• 2x – y = –4

• 10x – 5y = –20

• 7x = 39

• 13x = 39

EVALUATION

Here the given system of equations are

$\sf{2x - y = - 4} \: \: \: ......(1)$

$\sf{3x + 5y = 59} \: \: \: .......(2)$

Multiplying Equation (1) by 5 we get

$\sf{10x - 5y = - 20} \: \: \: ......(3)$

Adding Equation (2) and Equation (3) we get

$\sf{13x = 39} \: \: \: .....(4)$

Upto above information are provided by the given task

We now solve for x and y

From Equation (4) we get

$\sf{x = 3}$

From Equation (1) we get

$\sf{(2 \times 3) - y = - 4}$

$\sf{ \implies \: 6 - y = - 4}$

$\sf{ \implies \: y = 6 + 4}$

$\sf{ \implies \: y = 10}$

So the solution of the given system of equations is x = 3 & y = 10

Now Equation (4) can replace any of the equations given by Equation (1) & (2) to get the same result

Hence the correct option is

$\sf{13x = 39} \: \: \:$

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