Question

For questions 4-5, how many solutions does the system have?

4. -4y+4=x
2x+8y=8
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution

5. 6x+2=y
3y-18x=12
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution

Answer 1

Answer:

$\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}$

Step-by-step explanation:

$Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}$

$Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}$