Question

Given the equations 9x+3/4y=6 and 2x+1/2y=9, by what factor the equation to eliminate y and solve the system through linea would you multiply the second equation to eliminate y and solve the system through linear combinations?
Options;
A.) -4/3
B.) -3/4
C.) -3/2
D.) -7/2

Answer 1

C -3/2  

Just multiply the second equation by -3/2
this will make the y term = -3/4y 

so adding will eliminate the  y terms.

Answer 2

Answer:

$-\dfrac{3}{2}$

C is correct.

Step-by-step explanation:

Given: System of equation

$9x+\frac{3}{4}y=6$

$2x+\frac{1}{2}y=9$

We have to solve system of equation by eliminating y

So, first we will make the coefficient of y same with opposite sign.

Coefficient of y in first equation 3/4

Coefficient of y in 2nd equation 1/2

$LCM \ of\ \frac{3}{4}\ and\ \frac{1}{2}=\frac{3}{2}$

Multiply second equation by -3/2 to make coefficient of y same

$-\frac{3}{2}\cdot 2x-\frac{3}{2}\cdot \frac{1}{2}y=-\frac{3}{2}\cdot 9$

$-3x-\frac{3}{4}y=-\frac{27}{2}$

$9x+\frac{3}{4}y=6$

Add both equation and eliminate y

$-3x+9x=-\frac{27}{2}+6$

$6x=-\frac{15}{2}$

$x=-\frac{5}{4}$

Hence, We multiply by -3/2 to eliminate y and solve the system of equation.