Answer:
✏️COORDINATES
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B. Find three solutions for the linear equation 4x - 3y = 1, and plot the solutions as points on a coordinate plane.
Solution for x
4x - 3y = 14x−3y=1
4x = 1 + 3y4x=1+3y
\begin{gathered} x = \frac{1 + 3y}{4} \\ \end{gathered}
x=
4
1+3y
Solution for y
4x - 3y = 14x−3y=1
\text-3y= 1 - 4x-3y=1−4x
\begin{gathered} y = \text- \frac{\text-1 + 4x}{3} \\ \end{gathered}
y=-
3
-1+4x
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Solutions for column x
" y = 1 "
\begin{gathered} x = \frac{1 + 3(1)}{4} \\ \end{gathered}
x=
4
1+3(1)
\begin{gathered} x = \frac{1 + 3}{4} \\ \end{gathered}
x=
4
1+3
\begin{gathered} x = \frac{4}{4} \\ \end{gathered}
x=
4
4
x = 1x=1
\:
" y = 5 "
\begin{gathered} x = \frac{1 + 3(5)}{4} \\ \end{gathered}
x=
4
1+3(5)
\begin{gathered} x = \frac{1 + 15}{4} \\ \end{gathered}
x=
4
1+15
\begin{gathered} x = \frac{16}{4} \\ \end{gathered}
x=
4
16
x = 4x=4
\:
" y = 9 "
\begin{gathered} x = \frac{1 + 3(\text9)}{4} \\ \end{gathered}
x=
4
1+3(9)
\begin{gathered} x = \frac{1 + 27}{4} \\ \end{gathered}
x=
4
1+27
\begin{gathered} x = \frac{28}{4} \\ \end{gathered}
x=
4
28
x = 7x=7
\:
Solutions for column y
" x = 1 "
\begin{gathered} y = \text- \frac{1 - 4(1)}{3} \\ \end{gathered}
y=-
3
1−4(1)
\begin{gathered} y = \text- \frac{1 - 4}{3} \\ \end{gathered}
y=-
3
1−4
\begin{gathered} y = \text- \frac{\text-3}{3} \\ \end{gathered}
y=-
3
-3
y = 1y=1
\:
" x = 4 "
\begin{gathered} y = \text- \frac{1 - 4(4)}{3} \\ \end{gathered}
y=-
3
1−4(4)
\begin{gathered} y = \text- \frac{1 - 16}{3} \\ \end{gathered}
y=-
3
1−16
\begin{gathered} y = \text- \frac{\text-15}{3} \\ \end{gathered}
y=-
3
-15
y = 5y=5
\:
" x = 7 "
\begin{gathered} y = \text- \frac{1 - 4(7)}{3} \\ \end{gathered}
y=-
3
1−4(7)
\begin{gathered} y = \text- \frac{1 - 28}{3} \\ \end{gathered}
y=-
3
1−28
\begin{gathered} y = \text- \frac{\text-27}{3} \\ \end{gathered}
y=-
3
-27
y = 9y=9
Column (x, y)
x = 1, \, y = 1 \quad \large(1, \, 1)x=1,y=1(1,1)
x = 4, \, y = 5 \quad \large(4, \, 5)x=4,y=5(4,5)
x = 7, \, y = 9 \quad \large(7, \, 9)x=7,y=9(7,9)
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