
To solve for x, we have to remember to isolate the variable.

For 1/2, we can make that 0.5, since their values are equivalent. Our equation:

Let's distribute the 0.5 first.


Now, let's simplify the right side of the equation. We have to distribute the negative to 3x and 1.

Then, we simplify the entire expression.


Our equation now:

Let's add 3x to the right and 3x to the left to simplify the -3x on the right side of the equation.


Let's do the same thing we did in Step 3 to 1.5. Subtract 1.5 on both sides of the equation.


Finally, we divide both sides by 6 to isolate x.


Answer:
Y-5=-8/5 (x+3)
Step-by-step explanation:
I: y=(1/2)x+5
II: y=(-3/2)x-7
substitution:
fancy word for insert the definition of one variable in one equation into the other
-> isolate a variable, luckily y is isolated (even in both equations) already
-> substitute y of II into I (=copy right side of II and replace y in I with it):
(-3/2)x-7=(1/2)x+5
-3x-14=x+10
-3x-24=x
-24=4x
-6=x
-> insert x back into I (or II):
y=(1/2)x+5
=(1/2)*(-6)+5
=-3+5=2
elimination: subtract one equation from the other to eliminate a variable, again y is already isolated->no extra work required
I-II:
y-y=(1/2)x+5-[(-3/2)x-7]
0=(1/2)x+5+(3/2)x+7
0=(4/2)x+12
-12=2x
-6=x
-> insert x back into I (or II):
y=(1/2)x+5
=(1/2)*(-6)+5
=-3+5=2