Systems of Equations Question 7

For what value of $a$ does the system have no solution? $-3x+y=6$ $ax+2y=4$

\dfrac{1}{2}

-6

-3

3

Approach

For a system of linear equations to have no solution, they need to have the same slope and different $y$ -intercepts. Rearranging the two equations into slope-intercept form,

-3x+y=6

y=3x+6

ax+2y=4

2y=-ax+4

y=-\frac{a}{2}x+2

Setting the slopes equal to each other,

3=-\frac{a}{2}

\boxed{-6}=a