How do you solve a + b = 4 and 2a + 3b = 11 using substitution?

Feb 29, 2016

$a , b = 1 , 3$

Explanation:

$\textcolor{b l u e}{a + b = 4} , \textcolor{red}{2 a + 3 b = 11}$

Solve for first equation

$\rightarrow a + b = 4$

$\rightarrow b = 4 - a$

Substitute the value of $b$ to the second equation

$\rightarrow 2 \left(4 - a\right) + 3 b = 11$

$\rightarrow 8 - 2 b + 3 b = 11$

$\rightarrow 8 + b = 11$

$\rightarrow b = 11 - 8$

color(green)(rArrb=3

So substitute the value to the first equation

$\rightarrow a + 3 = 4$

$\rightarrow a = 4 - 3$

color(green)(rArra=1