Which statement correctly explains how Mari should find a solution to the following system of linear equations using elimination?

2f-5g=-9

-7f+3g=4

Multiply the first equation by 7 and the second equation by 2, and then add.

Multiply the first equation by 3 and the second equation by 5, and then subtract.

Multiply the first equation by –7 and the second equation by 2, and then add.

Multiply the first equation by –3 and the second equation by 5, and then add.

ANSWER

The correct answer is A.

EXPLANATION

The given systems of equations are

\(2f - 5g = - 9 - - (1)\)

\(
-7f+3g=4 - - (2)\)

If we multiply the first equation by 7 we get,

\(14f - 35g = - 63 - - (3)\)

If we multiply the
\(- 14f + 6g = 8 - - (4)\)

Adding equation (3) and (4) gives,

\(- 31g = - 55\)
We can see that f has been eliminated from the equation, and hence we can find g and use it to find f.

However, if we multiply the first equation by 3 and the second equation by 5, and then subtract, none of the variables will be eliminated.

Also, if we multiply the first equation by –7 and the second equation by 2, and then add, neither f nor g will be eliminated.

The same thing applies to multiplying the first equation by –3 and the second equation by 5, and then adding will not eliminate any of the variables.