Lesson 14

Making More New, True Equations

  • Let’s practice combining like terms and working with horizontal and vertical lines.

14.1: Criss Cross'll Make You Jump

Match each equation with its graph.

  • \(x=7\)
  • \(y=7\)
  • \(x+y=7\)


Y=7 graphed on Coordinate plane 


Graph of x=7 on coordinate plane 


Line graphed on coordinate plane. X intercept = 7. Y intercept =7. 


Graph of line. Passes through -2 comma-10 and origin 

14.2: They're Like Terms, Man

Rewrite each expression by combining like terms.

  1. \(11s-2s\)

  2. \(5t+3z-2t\)

  3. \(23s-(13t+7t)\)

  4. \(7t + 18r + (2r - 5t)\)
  5. \(\text{-}4x + 6r - (7x + 2r)\)
  6. \(3(c-5) + 2c\)
  7. \(8x - 3y + (3y - 5x)\)
  8. \(5x + 4y - (5x + 7y)\)
  9. \(9x - 2y - 3(3x+y)\)
  10. \(6x+12y + 2(3x-6y)\)

14.3: Finding More Lines

For each system of equations:

  • Solve the system of equations by graphing. Write the solution as an ordered pair.
  • Write an equation that would represented by a vertical or horizontal line that also passes through the solution of the system of equations.
  • Graph your new equation along with the system.
  1. \(\begin {cases} \begin {align}y = 3x+5\\ y=\text{-}x+1\end{align} \end {cases}\)

    The line representing \(y = 3x+5\) is shown

    Graph of y=3x +5
  2. \(\begin {cases} \begin {align}y = \frac{1}{3}x-2\\ y=x-6\end{align} \end {cases}\)

    The line representing \(y = \frac{1}{3}x-2\) is shown

    Graph of y = one third x - 2
  3. \(\begin {cases} \begin {align} 2x+3y=10\\ x+y=3\end{align} \end {cases}\)

    The line representing \(2x+3y=10\) is shown

    Graph of 2x -3y =10