How do you solve $3 a + b = 4$ $3a+b=4$ and $a - 2 b = 6$ $a-2b=6$ using substitution?

Question

How do you solve $3 a + b = 4$ $3a+b=4$ and $a - 2 b = 6$ $a-2b=6$ using substitution?

1 Answer

Impact of this question

3218 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-03T18:58:49

$(a, b) \to (2, - 2)$ $(a,b)to(2,-2)$

Explanation:

$3 a + b = 4 \to (1)$ $3a+b=4to(1)$

$a - 2 b = 6 \to (2)$ $a-2b=6to(2)$

$from equation (2) we obtain a = 6 + 2 b \to (3)$ $"from equation "(2)" we obtain "a=6+2bto(3)$

$substitute a = 6 + 2 b into equation (1)$ $color(blue)"substitute "a=6+2b" into equation "(1)$

$\Rightarrow 3 (6 + 2 b) + b = 4$ $rArr3(6+2b)+b=4$

$\Rightarrow 18 + 6 b + b = 4$ $rArr18+6b+b=4$

$\Rightarrow 18 + 7 b = 4$ $rArr18+7b=4$

$subtract 18 from both sides$ $"subtract 18 from both sides"$

$cancel(18)cancel(-18)+7b=4-18$

$rArr7b=-14$

$"divide both sides by 7"$

$(cancel(7) b)/cancel(7)=(-14)/7$

$rArrb=-2$

$color(blue)"substitute "b=-2" in equation "(1)$

$3a-2=4$

$rArr3a=4+2=6$

$rArra=6/3=2$

$"the solution is "a=2,b=-2$

Science

Math

Humanities

... and beyond

How do you solve $3 a + b = 4$ $3a+b=4$ and $a - 2 b = 6$ $a-2b=6$ using substitution?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 3a+b=43a+b=43a+b=4 and a-2b=6a−2b=6a-2b=6 using substitution?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $3 a + b = 4$ $3a+b=4$ and $a - 2 b = 6$ $a-2b=6$ using substitution?