Question

What is the value of the x variable in the solution to the following system of equations?

3x + 2y = 8
2x + 3y = 2

4

−2

x can be any number as there are infinitely many solutions to this system

There is no x value as there is no solution to this system

Answer 1

A couple of approaches you can take here. You can quickly graph the two lines. If the lines intersect, there is a unique solution, and it is the (x,y) of the point of intersection. To quickly graph the lines, alternately set x = 0 and solve for y, then set y = 0 and solve for x. You'll get two points (the x and y intercepts), draw a straight line through them. Repeat for the other equation.

If the lines turn out to be parallel, there are no solutions. If the lines turn out to be identical, there are infinitely many solutions.

Another approach would be to try the x values offered as answer choices, and solve for y. If the resulting (x,y) also satisfies the other equation, then you know your answer is either the point you tried, or infinitely many solutions. You'd have to investigate the latter possibility.

Solve by elimination or substitution. To solve by elimination, I would multiply one equation by 2 and the other by -3, then add them together. You'll get an equation in only 1 variable which you can solve.

To solve by substitution, solve one of the equations for x (or y, whatever seems easiest). Substitute that into the other equation to give an equation in only one variable. Solve.

Answer 2

so.... basically just graphing

Answer 3

To solve for x, you can eliminate either variable from the system of equations. multiply the first eq. by -2 and the second by 3. This will cancel out the x variable. Solve for y to get y=-2. Plug this back into one of the equations to get x=4

Answer 4

Graphing is one quick way to do it. But not the only way — read the rest of my post.

Answer 5

I, myself, prefer the elimination method.....but not everybody does. Do what is easier for you.