3.2 Substitution

Solving simultaneous equations by substitution

$\mathrm{3x}+\mathrm{4y}=1$

$\mathrm{2x}-y=8$

• The easiest variable to solve for here is the $y$ in the second equation.
  • $-y=-\mathrm{2x}+8$
  • $y=\mathrm{2x}-8$
• Now, we plug that into the other equation:
  • $\mathrm{3x}+4(\mathrm{2x}-8)=1$
• We now have an equation with only $x$ in it, so we can solve for $x$ .
  • $\mathrm{3x}+\mathrm{8x}-\text{32}=1$
  • $\text{11}x=\text{33}$
  • $x=3$
• Finally, we take the equation from step (1), $y=\mathrm{2x}-8$ , and use it to find $y$ .
  • $y=2(3)-8=-2$

So $(\mathrm{3,}-2)$ is the solution. You can confirm this by plugging this pair into both of the original equations.