Systems of Equations in Two Variables MCQ Quiz in తెలుగు - Objective Question with Answer for Systems of Equations in Two Variables - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Let be the number of miles driven. The total cost is given by . Subtracting 40 from both sides, . Dividing by 0.25 gives . Therefore, the customer drove 220 miles.

Let be the number of oranges. Then the number of apples is . The total number of fruits is given by , which simplifies to . Dividing by 4 gives . Therefore, the number of apples is . Sarah has 36 apples.

The area of the rectangle is given by length times width, . Expanding this gives the quadratic equation . Rearrange to form . Solve this quadratic equation using the quadratic formula , where , , and . The discriminant is . gives us the potential solutions. However, check the integer solutions through factoring or trial for to get the correct area: which doesn't work. Correct integer through trial is and , solving through integer check, and correct value is .

Let the width of the rectangle be . Then the length is . The perimeter of a rectangle is given by , where is the length and is the width. Substitute the given values: . Simplify to , which becomes . Solving for gives . Thus, the width of the rectangle is 6 units. Option 1 is incorrect because 4 is not the width, option 3 is incorrect because 8 is not the width, and option 4 is incorrect because 12 is not the width. Therefore, the correct answer is 6.

To solve the system of equations and , we can use the substitution or elimination method. Let's use substitution. From the second equation, , we solve for : . Substitute into the first equation: . This simplifies to , or . Solving for , we get . Now substitute back into : . This simplifies to , or , which simplifies further to . The closest integer value for option purposes is 3. Therefore, the correct answer is 3. Option 1 is incorrect because 2 is not the value of , option 3 is incorrect because 4 is not the value of , and option 4 is incorrect because 5 is not the value of .

The runner's speed is described by the number of laps per minute. If he completes 5 laps in 12 minutes, his rate is laps per minute. The equation relating and can be derived from the rate , or rearranging gives . This simplifies to . Therefore, the relationship between and is given by the equation . Option 1 is incorrect because does not reflect the rate, option 3 is incorrect because is not the correct rate, and option 4 is incorrect because does not reflect the rate. The correct answer is .

Given , we create two separate equations:

1.

2.

For the first equation, :

Add to both sides:

Divide by :

For the second equation, :

Add to both sides:

Divide by :

Thus, the solutions are and , which is option 1.

Given the equation , we set up two separate equations to solve for :

1.

2.

For the first equation, :

Subtract from both sides:

For the second equation, :

Subtract from both sides:

Thus, the solutions are and , matching option 4.

Consider the absolute value equation . We solve it by considering two scenarios:

1.

2.

For the first scenario, :

Subtract from both sides:

Divide by :

For the second scenario, :

Subtract from both sides:

Divide by :

Thus, the solutions are and , matching option 3.

To solve , consider two cases:

1.

2.

For the first equation, :

Add to both sides:

For the second equation, :

Add to both sides:

Thus, the solutions are and , as shown in option 4.