Question

1. Emma used elimination to solve this system of linear equations. 3x + 5y = -17 2x + 4y = 6 Which equation did Emma have after

Answer 1

EXPLANATION

Given the system of equations:

(1) 3x + 5y = -17

(2) 2x + 4y = 6

Multiplying (1) by 2 and (2) by 3:

(1) 6x + 10y = -34

(2) 6x + 12y = 18

Subtracting (2) to (1):

(2) 6x + 12y = 18

-

(1) 6x + 10y = -34

-------------------------------------

2y = 52

Dividing both sides by 2:

y = 52/2

Simplifying:

y = 26

`\mathrm{For\: }6x+10y=-34\mathrm{\: plug\: in\: }y=26`
`6x+10\cdot\: 26=-34`
`\mathrm{Multiply\: the\: numbers\colon}\: 10\cdot\: 26=260`
`6x+260=-34`
`\mathrm{Subtract\: }260\mathrm{\: from\: both\: sides}`
`6x+260-260=-34-260`

Simplify:

`6x=-294`

Divide both sides by 6:

`(6x)/(6)=(-294)/(6)`

Simplify:

`x=-49`

The solutions to the system of equations are:

`x=-49,\: y=26`