Question

Analyze the solution set of the following system by

following the given steps.
2x + y = 5
3y = 9 - 6x
Write each equation in slope-intercept form.
y =
y =
VE +
X +
DONE
For

Answer 1

Write each equation in slope-intercept form.

y = -2x + 5

y = -2x + 3

What do the equations have in common? How are they different?

- The slopes are the same.

- The y-intercepts are different.

The system represents lines that (are parallel),

therefore the system has no solution.

Answer 2

The equations in the slope-intercept form

y = - 2 x + 5

y = - 2 x + 3

Explanation:

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope of the line.

• b is the y-intercept.

To put any equation in the slope-intercept form state y on the left side, x and the numerical term on the right side, the coefficient of y must be 1.

Let us do that with the given equations

∵ 2x + y = 5

→ Subtract 2x from both sides to move x to the right sides

∴ 2x - 2x + y = 5 - 2x

∴ y = 5 - 2x

→ Switch 5 and - 2x

∴ y = - 2x + 5

∵ 3y = 9 - 6x

→ Divide each term by 3 to make the coefficient of y = 1

∴
`(3y)/(3)=(9)/(3)-(6x)/(3)`

∴ y = 3 - 2x

→ Switch 3 and - 2x

∴ y = - 2x + 3

The equations in the slope-intercept form

y = - 2x + 5

y = - 2x + 3