Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Find the missing coordinate to complete the ordered-pair solution to the given linear equation.

[tex]\[5x - 6y = 39\][/tex]

(a) [tex]\((-3, \, \square)\)[/tex]
(b) [tex]\((\square, \, 1)\)[/tex]


Sagot :

Sure! Let's solve the given linear equation [tex]\( 5x - 6y = 39 \)[/tex] and find the missing coordinates for each part.

### Part (a): Find the missing y-coordinate when [tex]\( x = -3 \)[/tex]

We start with the linear equation:
[tex]\[ 5x - 6y = 39 \][/tex]

Substitute [tex]\( x = -3 \)[/tex] into the equation:
[tex]\[ 5(-3) - 6y = 39 \][/tex]

Simplify the equation:
[tex]\[ -15 - 6y = 39 \][/tex]

Next, we isolate the term with [tex]\( y \)[/tex]:
[tex]\[ -6y = 39 + 15 \][/tex]
[tex]\[ -6y = 54 \][/tex]

Divide both sides by -6 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{54}{-6} \][/tex]
[tex]\[ y = -9 \][/tex]

Therefore, the ordered-pair solution is [tex]\( (-3, -9) \)[/tex].

### Part (b): Find the missing x-coordinate when [tex]\( y = 1 \)[/tex]

We start again with the same linear equation:
[tex]\[ 5x - 6y = 39 \][/tex]

Substitute [tex]\( y = 1 \)[/tex] into the equation:
[tex]\[ 5x - 6(1) = 39 \][/tex]

Simplify the equation:
[tex]\[ 5x - 6 = 39 \][/tex]

Next, we isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 5x = 39 + 6 \][/tex]
[tex]\[ 5x = 45 \][/tex]

Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{45}{5} \][/tex]
[tex]\[ x = 9 \][/tex]

Therefore, the ordered-pair solution is [tex]\( (9, 1) \)[/tex].

To summarize:

(a) The ordered-pair solution is [tex]\( (-3, -9) \)[/tex].

(b) The ordered-pair solution is [tex]\( (9, 1) \)[/tex].
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.