Question

Solve by graphing
x + 2y = 10
3x - 2y = 6

Answer 1

(4,3)

Explanation:

The solution to a system of linear equations is the coordinate point that makes both statements true.

Slope-Intercept

Both the equations above are in standard form, where both variables are on one side of the equation. While it is possible to graph this type of equation, it's very difficult. So, the first thing we should do is convert both equations to slope-intercept form. The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find slope-intercept form we need to isolate y.

Let's start with x + 2y = 10. First, subtract x from both sides.

• 2y = -x + 10

Then, divide by 2.

• y = -1/2x + 5

Next, let's convert 3x - 2y = 6. Start by subtracting 3x from both sides.

• -2y = -3x + 6

Then, divide by -2.

• y = 3/2x - 3

Graphing

Now, we can graph these lines. The solution to the system of equations is where the lines intersect. Below is the graph of these lines. As you can see, the lines intersect at (4,3). Thus, (4,3) is the solution. This means that both equations are true when x=4 and y=3.