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(a) Is the point (3, −5) on the line $5x + 3y + 6 = 0$? Justify your answer - Junior Cycle Mathematics - Question 5 - 2016

Question 5

(a) Is the point (3, −5) on the line $5x + 3y + 6 = 0$? Justify your answer. (b) Find the point of intersection of the following two lines. $3x + 2y = 7$ y = -2x ... show full transcript

Worked Solution & Example Answer:(a) Is the point (3, −5) on the line $5x + 3y + 6 = 0$? Justify your answer - Junior Cycle Mathematics - Question 5 - 2016

Step 1

Is the point (3, −5) on the line $5x + 3y + 6 = 0$?

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Answer

To determine if the point (3, −5) is on the line, we substitute $x = 3$ and $y = -5$ into the equation of the line:

$5(3) + 3(-5) + 6 = 0$

Calculating this:

$15 - 15 + 6 = 6$

Since the left side equals 6, not 0, the point (3, −5) is not on the line. Therefore, the answer is no, it does not satisfy the line equation.

Step 2

Find the point of intersection of the following two lines: $3x + 2y = 7$ and $y = -2x + 5$

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Answer

To find the point of intersection, we will substitute the expression for $y$ from the second equation into the first equation:

Substitute $y$ : $3x + 2(-2x + 5) = 7$
Simplify: $3x - 4x + 10 = 7$ $-x + 10 = 7$
Solve for $x$ : $-x = 7 - 10$ $-x = -3$ $x = 3$
Use the value of $x$ to find $y$ : $y = -2(3) + 5 = -6 + 5 = -1$

Thus, the point of intersection is $(3, -1)$ .

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