Question

Complete the table below and write your answer on a separate sheet of

paper.

1. {2x − 3y = −7
2x − 3y = 8

2. {x − y = −5
x + y = 1

3. {x + y = 1
3x + 3y = 3

Slope-intercept form ll Slope ll Y-intercep ll Number of Solutions ll Type of System of Linear Equation

1.

2.

3.

RIGHT ANSWER MAY BRAINLIEST

Answer 1

sorry I dont know the answer

Answer 2

Step-by-step explanation:

Given:

$1)2x - 3y = - 7 \\ 2x - 3y = 8$

$2) x - y = - 5 \\ x + y = 1$

$3)x + y = 1 \\ 3x + 3y = 3$

To find: Write Slope-intercept form ll Slope ll Y-intercept ll Number of Solutions ll Type of System of Linear Equation

Solution:

1)

$2x - 3y = - 7 \\ 2x - 3y = 8$

Slope intercept form

$\bf y = mx + c$

Thus,

Slope intercept form of line 1:$y = \frac{2}{3} x + \frac{7}{3}$

Slope intercept form of line 2:$y = \frac{2}{3} x - \frac{8}{3}$

Slope of line 1: $m_1 = \frac{2}{3}$

Slope of line 2:$m_2 = \frac{2}{3}$

Y- intercept of line 1:$(0, \: \frac{7}{3} )$

Y-intercept of line 2:$(0, - \frac{8}{3} )$

It is clear that both lines are parallel, because they are having same slope and different Y-intercept.

Number of solution: No solution

Type of system of linear equation: Inconsistent

2)

$x - y = - 5 \\ x + y = 1$

Slope intercept form:

eq1:$y = x + 5$

eq2:$y = - x + 1$

Slope of line 1:$m_1 = 1$

Slope of line 2:$m_2 = - 1$

Y-intercept of line 1:$(0,5)$

Y-intercept of line 2:$(0,1)$

No of solution: 1

Because, slope and Y-intercept are different,so lines are intersecting lines.

System of equations: Consistent (unique solution)

3)

$x + y = 1 \\ 3x + 3y = 3$

Slope intercept form:

eq1:$y = -x + 1$

eq2:$y = - x + 1$

Slope of line 1:$m_1 = -1$

Slope of line 2:$m_2 = - 1$

Y-intercept of line 1:$(0, 1)$

Y-intercept of line 2:$(0,1)$

No of solution: Infinitely many solutions

Because, slope and Y-intercept are same,so lines are coincident lines.

System of equations: Consistent (infinite solutions)

Hope it will help you.

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