Question

Solve each system by graphing and write the solution.y = -2x + 2y = 1/2x -3

Answer 1

Answer:

x = 2, y = -2

Explanation:

The system of equations is:

$\begin{gathered} y=-2x+2\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ y=\frac{1}{2}x-3\ldots\ldots\ldots\ldots.\ldots\ldots(2) \end{gathered}$

For the line y = -2x + 2

To find the x-intercept, let y = 0

0 = -2x + 2

2x = 2

x = 2/2

x = 1

The x-intercept = (1, 0)

To find the y-intercept, let x = 0

y = -2(0) + 2

y = 2

The y-intercept = (0, 2)

For the line y = 1/2 x - 3

To find the y-intercept, let x = 0

y = 1/2(0) - 3

y = -3

The y-intercept = (0, -3)

To find the x-intercept, let y = 0

0 = 1/2 x - 3

1/2 x = 3

x/2 = 3

x = 6

The x-intercept = (6, 0)

Plot the graphs of the two lines by taking into consideration the x and y intercepts

The equation y = -2x + 2 is plotted in red

The equation y = 1/2 x - 3 is plotted in blue

The point where the two lines meet is the solution to the system of equations

The two lines meet at the point (2, -2)

Therefore, the solution to the system of equations is:

x = 2, y = -2