Answer:
1) [tex]x=\dfrac12[/tex]
2) [tex]n = -3 \ \ \textsf{and} \ \ m = -4[/tex]
3) see below
4) A: 0 = 1
Step-by-step explanation:
Question 1
[tex]15-0.5(4x-2)+4x=17[/tex]
[tex]\implies 15-2x+1+4x=17[/tex]
[tex]\implies 2x+16=17[/tex]
[tex]\implies 2x=1[/tex]
[tex]\implies x=\dfrac12[/tex]
Question 2
[tex]\textsf{rearrange} \ n=m+1 :[/tex]
[tex]\implies -m=-n+1[/tex]
[tex]\textsf{add equations} \ -m=-n+1 \ \textsf{and} \ m=2n+2:\\[/tex]
[tex]\implies0=n+3[/tex]
[tex]\implies n=-3[/tex]
[tex]\textsf{substitute} \ \ n=-3 \ \ \textsf{into} \ \ m=n-1:[/tex]
[tex]\implies m=-3-1[/tex]
[tex]\implies m=-4[/tex]
Question 3
subtract the second equation from the first
divide both sides by -4
substitute found value for y into first equation
solve for x
Question 4
[tex]3j=k[/tex]
[tex]k=3j+1[/tex]
[tex]\textsf{rearrange} \ 3j=k :[/tex]
[tex]\implies -k=-3j[/tex]
[tex]\textsf{add equations}\ -k=-3j \ \ \textsf{and}\ \ k=3j+1:[/tex]
[tex]\implies 0=1[/tex]
Solution = A
