how to solve ?

Question

how do you you use the graphing & addition method for this problem  

2x-y=7

-x+2y=-5

Answer 1

Substitution method :

The system of equations are 2x - y = 7 and - x + 2y = - 5.

Solve the equation 1: 2x - y = 7 for y, since the y has a coefficient of - 1.

2x - y = 7

- y = 7 - 2x

y = 2x - 7.

Substitute the value of y = 2x - 7 in the equation 2: - x + 2y = - 5 and solve for x.

- x + 2(2x - 7) = - 5

- x + 4x - 14 = - 5

3x - 14 = - 5

3x = - 5 + 14

3x = 9

x = 9/3

x = 3.

Substitute the value of x = 3 in the equation y = 2x - 7 to find the value of y.

y = 2(3) - 7

y = 6 - 7

y = - 1.

The solution of the system is x = 3 and y = - 1.

Graphing method :

Write the equations in slope-intercept form y = mx + b, where m is slope and b is y - intercept.

The first equation is 2x - y = 7.

- y = - 2x + 7

y = 2x - 7.

Compare the equation with slope-intercept form y = mx + b.

slope = 2 and y-intercept is - 7.

y-intercept is - 7, so the line crosses the y-axis at (0, - 7)

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, - 7), move 2 units up and 1 unit right, then plot the point (1, - 5).

The second equation is - x + 2y = - 5.

2y = x - 5

y = (1/2)x - (5/2).

Compare the equation with slope-intercept form y = mx + b.

slope = 1/2 and y-intercept is - 5/2(2. 5).

y-intercept is - 2. 5, so the line crosses the y-axis at (0, - 2. 5)

Using slope find the next point.

Slope = rise/run = 1/2

Start at point (0, - 2. 5), move 1 unit up and 2 units right, then plot the point (2, -1. 5).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the system (x, y ) = (3, - 1).