Question

Solve the system using subsitution.

1.{4x−y=−3

y=5x


2.{6x−y=−15
x+2y=17

3. {11c−2d=−2
c+8d=8

Answer 1

`1.\ x=3\ and\ y=15\\\\2.\ x=-1\ and\ y=9\\\\3.\ c=0\ and\ d=1`

Explanation:

`1.\\\left\{\begin{array}{ccc}4x-y=-3&(1)\\y=5x&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\4x-5x=-3\\-x=-3\qquad\text{change the signs}\\\boxed{x=3}\\\\\text{Put the vallue of x to (2):}\\\\y=5(3)\\\boxed{y=15}`

`2.\\\left\{\begin{array}{ccc}6x-y=-15\\x+2y=17&\text{subtract 2y from both sides}\end{array}\right\\2.\\\left\{\begin{array}{ccc}6x-y=-15&(1)\\x=17-2y&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\6(17-2y)-y=-15\qquad\text{use distributive property}\\(6)(17)+(6)(-2y)-y=-15\\102-12y-y=-15\qquad\text{substract 102 from both sides}\\-13y=-117\qquad\text{divide both sides by (-13)}\\\boxed{y=9}\\\\\text{Put the value of y to (2):}\\\\x=17-2(9)\\x=17-18\\\boxed{x=-1}`

`3.\\2.\\\left\{\begin{array}{ccc}11c-2d=-2\\c+8d=8&\text{substract 8d from both sides}\end{array}\right\\\left\{\begin{array}{ccc}11c-2d=-2&(1)\\c=8-8d&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\11(8-8d)-2d=-2\qquad\text{use distributive property}\\(11)(8)+(11)(-8d)-2d=-2\\88-88d-2d=-2\qquad\text{subtract 88 from both sides}\\-90d=-90\qquad\text{divide both sides by (-90)}\\\boxed{d=1}\\\\\text{Put the value of d to (2):}\\\\c=8-8(1)\\c=8-8\\\boxed{c=0}`