More to Explore

Solve for the Value of Each Shape with Three Variables Solutions

Use the shape version of the work provided below as a guide to solve for the value of each shape.

square: x, triangle: y, circle: z

$3 x = z x + y + z = 19 2 z - 1 = y$

$z = 3 x y = 2 z - 1$

$x + (2 z - 1) + 3 x = 19$

  $\begin{array}{rcl} 4 x + 2 (3 x) - 1 & = & 19 \\ 4 x + 6 x & = & 20 \\ 10 x & = & 20 \\ x & = & 2 \\ z & = & 3 (2) = 6 \\ y & = & 2 (6) - 1 = 11 \\ (2, 11, 6) \end{array}$

Solve for the value of each shape.

$c + r + t = 0 2 c + r = - 1 2 c - 4 t = 2$  

$\begin{array}{ccl} - 1 (c + r + t = 0) & \Rightarrow & - c - r - t = 0 \\ + 2 c + r = - 1 \\ c - t = - 1 \end{array}$

$\begin{array}{ccl} - 2 (c - t = - 1) & \Rightarrow & - 2 c + 2 t = 2 \\ + 2 c - 4 t = 2 \\ - 2 t = 4 \\ t = - 2 \end{array}$

$\begin{array}{rcl} c - (- 2) & = & - 1 \\ c + 2 & = & - 1 \\ c & = & - 3 \end{array}$

$\begin{array}{rcl} - 3 + r - 2 & = & 0 \\ r & = & 5 \end{array}$

Circle = –3, rectangle = 5, triangle = –2