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

Answer:

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: $-\frac{1}{2}$ is used to eliminate the x-terms when adding with the second equation.

Part c: $\frac{1}{2}$ 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.

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 $-\frac{1}{2}$ 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, $-\frac{1}{2}$ 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 $\frac{1}{2}$ 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, $\frac{1}{2}$ 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.