Answer:
4/7= 12/21- mutiply the fraction by 3
(4)(3)/(7/(3)= 12/21
4/7= 16/28 - mutiply by 4
4/7= 20/35- mutiply by 5
The solution to given system of equations is x = 2 and y = -5
<em><u>Solution:</u></em>
<em><u>Given the system of equations are:</u></em>
4x + y = 3 ---------- eqn 1
-2x + 3y = -19 ---------- eqn 2
We have to find the solution to above system of equations
<em><u>We can solve the system by substitution method</u></em>
From eqn 1,
4x + y = 3
Isolate y to one side
y = 3 - 4x ----------- eqn 3
<em><u>Substitute eqn 3 in eqn 2</u></em>
-2x + 3(3 - 4x) = -19
-2x + 9 - 12x = -19
Combine the like terms
-14x = -19 - 9
-14x = -28
Divide both sides of equation by -14
<h3>x = 2</h3>
<em><u>Substitute x = 2 in eqn 3</u></em>
y = 3 - 4(2)
y = 3 - 8
<h3>y = -5</h3>
Thus the solution is x = 2 and y = -5
To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, a
diagram showing the lines and their common transversal is attached.
The completed two column proof is presented as follows;
Statement
Reason
1. ∠1 and ∠2 are supplementary angles
1. Given
2. m∠1 + m∠2 = 180°
2. <u>Definition of supplementary ∠s</u>
3. ∠1 and ∠3 are supplementary angles
3. Exterior sides in opposite rays
4. <u>m∠1 + m∠3 = 180° </u>
4. <u>Definition of supplementary ∠s</u>
5. m∠1 + m∠2 = m∠1 + m∠3
5. <u>Transitive property of equality</u>
6. <u>m∠2 = m∠3 </u>
6. <u>Subtraction property of equality</u>
7. l ║ m
7. <u>Converse of alternate interior </u>
<u>angles postulate</u>
Reasons:
- Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°
- Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)
- Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles
- Reason for statement 5: Transitive property of equality describes the property that if a number <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.
- Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality
- Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.
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We can use the vertical angle theorem which states that any two opposite angles are congruent. So, you can just set the two measures equal to each other and solve for x:




So, your answer is
20°.
Answer:

Step-by-step explanation:
Use the slope-intercept formula:
where m is slope and b the y-intercept.

Use the slope formula for when you have two points:

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

Simplify parentheses (negative+negative=positive)

Simplify

2 is the slope:

Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:
(4,7)


The y-intercept is -1. Insert into the equation. Change the + symbol to -:

Done.