Question

Question: which of the following represents the graph of the system of equations shown below:

x+y=3
5x-6y=6

Answer 1

graph A

Explanation:

Dividing by the constant on the right lets you put each equation into intercept form:

x/3 + y/3 = 1

x/1.2 +y/(-1) = 1

These tell you the first equation has x- and y- intercepts of 3, so only graph A is appropriate. The second equation has an x-intercept of 1.2 and a y-intercept of -1, which also agrees with graph A.

_____

Intercept form is ...

x/x-intercept + y/y-intercept = 1

Answer 2

graph A

Explanation:

Dividing by the constant on the right lets you put each equation into intercept form:

• x/3 + y/3 = 1
• x/1.2 +y/(-1) = 1

These tell you the first equation has x- and y- intercepts of 3, so only graph A is appropriate. The second equation has an x-intercept of 1.2 and a y-intercept of -1, which also agrees with graph A.

_____

Intercept form is ...

x/x-intercept + y/y-intercept = 1

I find this form convenient for graphing when the equation is originally in standard form, as these are.