Question

Solve each system by substitution.

4x+2y=10
x-y=13​

Answer 1

x = 6 and y = -7 → (6, -7)

Explanation:

`\left\{\begin{array}{ccc}4x+2y=10\\x-y=13&\text{add y to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}4x+2y=10&(1)\\x=y+13&(2)\end{array}\right\\\\\\\text{Substitute (2) to (1):}\\\\4(y+13)+2y=10\qquad\text{use the distributive property}\\\\(4)(y)+(4)(13)+2y=10\\\\4y+52+2y=10\qquad\text{subtract 52 from both sides}\\\\6y=-42\qquad\text{divide both sides by 6}\\\\\boxed{y=-7}\\\\\text{Put the value of y to (2):}\\\\x=-7+13\\\\\boxed{x=6}`

Answer 2

x-y=13

x=13+y--(1)

4x+2y=10

2x+y=5

26+2y+y=5

3y=-21

y=-7

Substituting value of y in equation (1)

x=13-7

x=6