Question

-x+7y=5,-4x+y=-7 System of equations substitution

Answer 1

Answer:

x = 2, y = 1 → (2, 1)

Step-by-step explanation:

$\left\{\begin{array}{ccc}-x+7y=5\\-4x+y=-7&\text{add}\ 4x\ \text{to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-x+7y=5&(1)\\y=4x-7&(2)\end{array}\right\qquad\text{subtritute (2) to (1)}\\\\-x+7(4x-7)=5\qquad\text{use the distributive property}\\\\-x+(7)(4x)+(7)(-7)=5\\\\-x+28x-49=5\qquad\text{add 49 to both sides}\\\\-x+28x=5+49\qquad\text{combine like terms}\\\\27x=54\qquad\text{divide both sides by 27}\\\\\boxed{x=2}$

$\text{Put the value of}\ x\ \text{to (2):}\\\\y=4(2)-7\\\\y=8-7\\\\\boxed{y=1}$