2. Objectives:
illustrate linear equations in two
variables;
determine if an ordered pair is a
solution of the given linear
equation;
graph linear equations in two
variables.
3. Determine whether or not each equation is a linear
equation in two variables. If yes, write it in
standard form.
5x + 3y = 6 Yes
Already in
standard form
4. Determine whether or not each equation is a linear
equation in two variables. If yes, write it in
standard form.
x = 7y + 3
x – 7y = 7y – 7y + 3
x – 7y = 3
Yes
Standard form
5. Determine whether or not each equation is a linear
equation in two variables. If yes, write it in
standard form.
3x2 – y = 9 No
6. Determine whether or not each equation is a linear
equation in two variables. If yes, write it in
standard form.
3
𝑥
+ 𝑦 = 20
No
7. Determine whether or not each equation is a linear
equation in two variables. If yes, write it in
standard form.
xy = -5 No
8. Determine whether or not each equation is a linear
equation in two variables. If yes, write it in
standard form.
𝑥
3
+
𝑦
6
= 1 Yes
9. Solutions of a Linear Equations in
Two Variables
These are ordered pairs (x, y) that
make the equation true.
10. Determine whether (3, -2) is a solution of
the equation 5y = -2x – 4.
5y = -2x – 4
5(-2) = -2(3) – 4
-10 = -6 – 4
-10 = -10 YES
11. Determine whether (-1, 4) is a solution of
the equation 6x + 2y = 3
6x + 2y = 3
6(-1) + 2(4) = 3
-6 + 8 = 3
2 ≠ 3 NO
23. x – intercept is the point where a line
crosses the x - axis
To solve for the x – intercept, let y = 0 and solve
for x.
Example: Find the x – intercept of x - 2y = 4
y = 0
x – 2(0) = 4
x = 4
The graph of x – 2y = 4 will cross the x – axis at
24. y – intercept is the point where a line
crosses the y - axis
To solve for the y – intercept, let x = 0 and solve
for y.
Example: Find the y – intercept of x - 2y = 4
x = 0
0 – 2𝑦 = 4
−2𝑦
−2
=
4
−2
y = - 2
