How do you solve the simultaneous equations $a + 5 = b$ $a+5=b$ and $2 a + 3 b = 6$ $2a+3b=6$ ?

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Answer 1 · 2018-03-26T10:13:17

$a = - \frac{9}{5}$ $a=-9/5$
$b = \frac{16}{5}$ $b=16/5$

I sub one of the equations into the other.

$b = a + 5$ $b=a+5$
$2 a + 3 b = 6$ $2a+3b=6$

therefore

$2 a + 3 (a + 5) = 6$ $2a +3(a+5)=6$
$2 a + 3 a + 15 = 6$ $2a + 3a + 15=6$
$5 a = - 9$ $5a = -9$
$a = - \frac{9}{5}$ $a=-9/5$

$b = 5 - \frac{9}{5}$ $b=5-9/5$
$b = \frac{16}{5}$ $b=16/5$

I used substitution method, in other cases it can be easier to use what's known as elimination.

How do you solve the simultaneous equations a+5=ba+5=b and 2a+3b=62a+3b=6?