Question

match each system to the number the first equation can be multiplied by to eliminate the x-terms when adding the second equation

Answer 1

1. 10x-4y=-8 matches: 1/2

-5x+6=10

2. -2x+6y=3 matches: 2

4x+3y=9

3. 3x-8y=1 matches: -2

6x+5y=12

4. -8x+10y=16 matches: -1/2

-4x-5y=13

Answer 2

Part a: -2 is used to eliminate the x-terms when adding with the second equation.

Part b:
`-(1)/(2)` is used to eliminate the x-terms when adding with the second equation.

Part c:
`(1)/(2)` is used to eliminate the x-terms when adding with the second equation.

Part d: 2 is used to eliminate the x-terms when adding with the second equation.

Step-by-step explanation:

Part a: The equations are
`3 x-8 y=1` and
`6 x+5 y=12`

To eliminate the x-terms from both the equations, let us multiply -2 with the first equation and hence it becomes
`-6x+16y=-2`

Adding the two equation, we get,

`-6x+16y+6 x+5 y=-2+12`

Simplifying, we get,

`21y=10`

Thus, the x-terms are eliminated when adding the equations.

Hence,-2 is used to eliminate the x-terms when adding with the second equation.

Part b: The equations are
`-8 x+10 y=16` and
`-4 x-5 y=13`

To eliminate the x-terms from both the equations, let us multiply
`-(1)/(2)` with the first equation and hence it becomes
`4 x-5 y=-8`

Adding the two equation, we get,

`4x-5y-4x-5y=-8+13`

Simplifying, we get,

`0=5`

Thus, the x-terms are eliminated when adding the equations.

Hence,
`-(1)/(2)` is used to eliminate the x-terms when adding with the second equation.

Part c: The equations are
`10 x-4 y=-8` and
`-5 x+6 y=10`

To eliminate the x-terms from both the equations, let us multiply
`(1)/(2)` with the first equation and hence it becomes
`5x-2y=-4`

Adding the two equation, we get,

`5x-2y-5x+6y=-4+10`

Simplifying, we get,

`4y=6`

Thus, the x-terms are eliminated when adding the equations.

Hence,
`(1)/(2)` is used to eliminate the x-terms when adding with the second equation.

Part d: The equations are
`-2 x+6 y=3` and
`4 x+3 y=9`

To eliminate the x-terms from both the equations, let us multiply 2 with the first equation and hence it becomes
`-4x+12y=6`

Adding the two equation, we get,

`-4x+12y+4x+3y=6+9`

Simplifying, we get,

`15y=15`

Thus, the x-terms are eliminated when adding the equations.

Hence, 2 is used to eliminate the x-terms when adding with the second equation.