Answered

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10. Does the system of equations 3x - 4y = 10 and y = 3/4x + 3 have onesolution, infinitely many solutions, or no solution? *O one solutioninfinitely many solutionsno solution

10 Does The System Of Equations 3x 4y 10 And Y 34x 3 Have Onesolution Infinitely Many Solutions Or No Solution O One Solutioninfinitely Many Solutionsno Solutio class=

Sagot :

Given the equations:

[tex]\begin{gathered} (1)3x-4y=10 \\ (2)y=\frac{3}{4}x+3 \end{gathered}[/tex]

To solve the system, follow the steps below.

Step 01: Write the equations in the slope-intercept form.

An equation in the slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

So, let's write the first equation using this form. To do it, let's subtract 3x from both sides.

[tex]\begin{gathered} 3x-4y-3x=10-3x \\ -4y=-3x+10 \end{gathered}[/tex]

Now, let's divide both sides by -4.

[tex]\begin{gathered} \frac{-4}{-4}y=\frac{-3x+10}{-4} \\ y=\frac{3}{4}x-\frac{10}{4} \end{gathered}[/tex]

The second equation is already in the slope-intercept form.

Step 02: Compare both equations.

[tex]\begin{gathered} (1)\frac{3}{4}x-\frac{10}{4} \\ (2)\frac{3}{4}x+3 \end{gathered}[/tex]

As can be seen, both have the same slope and different y-intercepts.

It is known that parallel lines have the same slope and different y-intercepts.

So, the lines are parallel.

A system of parallel lines has no solution since the lines do not have an interception point.

Answer: No solution.

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