Use the Substitution Method to solve the following system of equations.
2x + y = 3
-3x + 4y = 1

Question

Use the Substitution Method to solve the following system of equations.
2x + y = 3
-3x + 4y = 1

anonymous · Answer

Substitution means, solve for one variable and plug the resulting expression in place of it in another variable.
$$
\begin{array}{rclcrcl}
2x + y &=& 3 \
 y &=& 3-2x \
\
-3x + 4y &=& 1 & \text{substitute:}&  y &=& 3-2x\
-3x + 4(3-2x) &=& 1 & \text{solve for x} \
-3x + 12-8x &=& 1 \
-3x -8x &=& -11 \
-11x &=& -11 \
x &=& 1 \
\

2x + y &=& 3  &\text{substitute:}&  x &=& 1\
2(1) + y &=& 3  & \text{solve for y} \
y &=& 1\
\

&&&\text{solution}&(x, y) &=& (1, 1)
\end{array}
$$