Substitution Method

How do you solve the system with the substitution method?
x - y = 10
-x - y = 20

---

x - y = 10
-x - y = 20

x = y + 10 {added y to each side of top equation}

-(y + 10) - y = 20   {substituted (y + 10), in for x, into bottom equation}
-y - 10 - y = 20   {distributed negative sign through parentheses}
-2y - 10 = 20   {combined like terms}
-2y = 30   {added 10 to each side}
y = -15   {divided each side by -2}

x = y + 10  {transformed top equation}
x = -15 + 10   {substituted -15, in for y, into new top equation}
x = -5   {combined like terms}

x = -5 and y = -15

- Algebra House