x+y=3 -4x-4y=12

Answer 1

x + y = 3

-4x – 4y = 12

When you see that each term of an equation has a common factor, you can divide by that factor and get a simpler equation. I'm going to divide the second equation by –4.

-4x – 4y = 12

x + y = –3

Now the two equations are below. The two equations are similar but not identical.

x + y = 3

x + y = –3

When you are asked to solve a system of two or more equations, you are being asked to find where the graphs of the equations intersect. Another way to say this is that you are being asked to find an xy-pair that satisfies each equation. (x,y) will be the point where the two lines intersect.

You can solve this equation by graphing, by elimination, or by substitution. Or you can use logic and an understanding of algebra or slope.

Some lines do not intersect, because they are parallel. Parallel lines have the same slope. The slope can be identified by the coefficient in front of the x-term when the equation is written in slope-intercept form. I will rewrite the two equations in that form.

y = –x +3

y = –x –3

The slope is –1 for each of these lines. This means that they are parallel. There is NO solution to the system of equations of the two lines, because NO point is on BOTH lines; they have NO points in common.