$\"\"$

The equation are inslope-intercept form y = mx + b.

Make a table to find the solution that satisfies both equations.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
x
\ \
y₁ = 2x + 9
\ \
y₁
\ \
y₂ = –x + 3
\ \
y₂
\ \
(x₁, y₁)
\ \
(x₂, y₂)
\
\
–1
\ \
y₁ = 2(–1) + 9
\ \
7
\ \
y₂ = (–1) (–1) + 3
\ \
4
\ \
(–1, 7)
\ \
(–1, 4)
\
\
0
\ \
y₁ = 2(0) + 9
\ \
9
\ \
y₂ = (–1) (0) + 3
\ \
3
\ \
(0, 9)
\ \
(0, 3)
\
\
1
\ \
y₁ = 2(1) + 9
\ \
11
\ \
y₂ = (–1) (1) + 3
\ \
2
\ \
(1, 11)
\ \
(1, 2)
\
\
–1
\ \
y₁ = 2(–2) + 9
\ \
5
\ \
y₂ = (–1) (–2) + 3
\ \
6
\ \
(–2, 5)
\ \
(–2, 5)
\
\

Since the ordered pair $\"\"$ satisfying the both equations, the solution of the sysytem is $\"\"$ .

$\"\"$

The solution of the sysytem is $\"\"$ .

\ x \	\ y₁ = 2x + 9 \	\ y₁ \	\ y₂ = –x + 3 \	\ y₂ \	\ (x₁, y₁) \	\ (x₂, y₂) \
\ –1 \	\ y₁ = 2(–1) + 9 \	\ 7 \	\ y₂ = (–1) (–1) + 3 \	\ 4 \	\ (–1, 7) \	\ (–1, 4) \
\ 0 \	\ y₁ = 2(0) + 9 \	\ 9 \	\ y₂ = (–1) (0) + 3 \	\ 3 \	\ (0, 9) \	\ (0, 3) \
\ 1 \	\ y₁ = 2(1) + 9 \	\ 11 \	\ y₂ = (–1) (1) + 3 \	\ 2 \	\ (1, 11) \	\ (1, 2) \
\ –1 \	\ y₁ = 2(–2) + 9 \	\ 5 \	\ y₂ = (–1) (–2) + 3 \	\ 6 \	\ (–2, 5) \	\ (–2, 5) \