Answer:
a = -6/5
Step-by-step explanation:
For the graphs to be parallel the graphs should have same slope(m)
So we rewrite both our equations in the slope-intercept form then compare the slope to find the value of a like this,
[tex]y=mx+b[/tex]
This equation is the slope-intercept form we convert both our equations in this form firstly taking equation 1
[tex]5y=-2x+10\\\\y=\frac{-2x+10}{5} \\\\y=\frac{-2}{5}x+\frac{10}{5} \\\\y=\frac{-2}{5}x+2[/tex]
so if we compare it with y = mx + b the coefficient of x is m and hence
m= -2/5 now solving for equation 2
[tex]3y=ax-15\\\\y=\frac{ax-15}{3} \\\\y=\frac{ax}{3}-\frac{15}{3} \\\\y=\frac{a}{3}x-5\\\\[/tex]
so here if we compare it with y = mx + b the coeffienct of x is a/3 so since parallel lines have same slope by the formula:
[tex]m_1=m_2[/tex]
we equation both the slope to each other to find the value of a like this,
[tex]m_1=m_2\\\\\frac{-2}{5}=\frac{a}{3}\\\\-2(3)=a(5)\\\\-6=5a\\-6/5=a[/tex]
so the value of a equals
a= -6/5
