## Big Ideas Math Algebra 1 Student Journal 1st Edition Chapter 5 Solving Systems Of Linear Equations

**Page 131 Exercise 1 Answer**

**Given:** An equation y + 2 = x

To graph the equation

Identify the slope and y-intercept of the line and make a table of values to graph the given equation.

The given equation is y + 2 = x

Bring the equation in slope-intercept form.

Subtract 2 from both sides

y = x − 2

Comparing this equation with the slope-intercept form we get

The slope of the line is 1

The y-intercept of the line is−2

Make a table of values.

**Read and Learn More Big Ideas Math Algebra 1 Student Journal 1st Edition Solutions**

**Plot these points and graph the equation.**

**The graph of the equation y + 2 = x is**

**Page 131 Exercise 2 Answer**

**Given:** An equation 2x − y = 3

To graph the equation

Identify the slope and y-intercept of the line and make a table of values to graph the given equation.

The given equation is 2x −y = 3

Bring the equation in slope-intercept form.

Subtract 3 from both sides

2x−3 = y

y = 2x−3

Comparing this equation with the slope-intercept form we get, The slope of the line is 2

The y-intercept of the line is−3

Make a table of values.

**Plot these points and graph the equation.**

**The graph of the equation 2x−y = 3 is**

**Page 131 Exercise 3 Answer**

**Given:** An equation 5x +2y = 10

To graph the equation

Identify the slope and y-intercept of the line and make a table of values to graph the given equation.

The given equation is 5x + 2y = 10

Bring the equation in slope-intercept form.

Subtract 5x from both sides

2y=−5x + 10

Divide by 2

y=\(\frac{-5}{2} x\)+5

Comparing this equation with the slope-intercept form we get, The slope of the line is\(\frac{-5}{2} \), and the y-intercept of the line is 5

Make a table of values.

**Plot these points and graph the equation.**

**The graph of the equation 5x+2y=10 is**

**Page 131 Exercise 4 Answer**

**Given:** An equation y−3 = x

To graph the equation

Identify the slope and y-intercept of the line and make a table of values to graph the given

The given equation is y−3=x

Bring the equation in slope-intercept form.

Add 3 on both sides

y=x+3

Comparing this equation with the slope-intercept form we get, The slope of the line is 1

Make a table of values.

**Plot these points and graph the equation.**

**The graph of the equation y−3=x is**

**Page 131 Exercise 5 Answer**

**Given:** An equation 3x−y = −2

Identify the slope and y-intercept of the line and make a table of values to graph the given equation.

The given equation is 3x−y = −2

Bring the equation in slope-intercept form.

Add 2 on both sides

3x + 2 = y

That is, y=3x + 2

Comparing this equation with the slope-intercept form we get, The slope of the line is 3

The y-intercept of the line is 2

Make a table of values.

**Plot these points and graph the equation.**

**The graph of the equation 3x−y=−2 is**

**Page 131 Exercise 7 Answer**

**Given:** An inequality a−3>−2

To graph the solution.

Simplify the inequality so that the variable is on one side and then graph the solution keeping in mind that open circles are used for numbers that are less than or greater than and closed circles are used for numbers that are less than or equal to and greater than or equal to.

The given inequality is a−3>−2

To simplify the inequality

Add 3 on both sides of the equation

a>−2 + 3

Simplify, a>1

The number line is drawn with an open dot at 1 because the inequality used is greater than.

**The graph of the solution of the inequality a−3>−2 is**

**Page 131 Exercise 8 Answer**

**Given:** An inequality −4≥−2c

To graph the solution.

Simplify the inequality so that the variable is on one side and then graph the solution keeping in mind that open circles are used for numbers that are less than or greater than and closed circles are used for numbers that are less than or equal to and greater than or equal to.

The given inequality is −4≥−2c

To simplify the inequality

Divide by 2 into both sides

\(\frac{-4}{2} \geq \frac{-2}{2} c\)

Simplify, −2≥−c

Multiplying by−1 reverses the sign of inequality.

2≤c

⇒ c≥2

The number line is drawn with a closed dot at 2 because the inequality used is greater than or equal to.

**The graph of the solution of the inequality −4≥−2c is**

**Page 131 Exercise 9 Answer**

**Given:** An inequality 2d−5<−3

To graph the solution.

Simplify the inequality so that the variable is on one side and then graph the solution keeping in mind that open circles are used for numbers that are less than or greater than and closed circles are used for numbers that are less than or equal to and greater than or equal to.

The given inequality is 2d−5<−3

To simplify the inequality

Add 5 on both sides

2d<−3 + 5

2d<2 (Divide by 2)

2d ÷ 2 < 2 ÷ 2

d<1

The number line is drawn with an open dot at 1 because the inequality used is less than.

**The graph of the solution of the inequality 2d−5<−3 is**

**Page 131 Exercise 10 Answer**

**Given:** An inequality 8−3r≤5−2r

Simplify the inequality so that the variable is on one side and then graph the solution keeping in mind that open circles are used for numbers that are less than or greater than and closed circles are used for numbers that are less than or equal to and greater than or equal to.

The given inequality is 8−3r≤5−2r

To simplify the inequality

Add 3r on both sides

8≤5−2r + 3r

Subtract 5 from both sides

8−5≤r

Simplify

3≤r

That is, r≥3

The number line is drawn with a closed dot at 3 because the inequality used is greater than or equal to.

**The graph of the solution of the inequality 8−3r≤5−2r is**