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

-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 - 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*