An unknown number y is 10 more than an unknown number x.

Mathematics
Tutor: None Selected Time limit: 1 Day

An unknown number y is 10 more than an unknown number x. The number y is also x less than 3. The equations to find x and y are shown below. 


y = x + 10 
y = −x + 3 

Which of the following statements is a correct step to find x and y?

Add the equations to eliminate x.

Multiply the equations to eliminate y.

Write the points where the graphs of the equations intersect the x-axis.

Write the points where the graphs of the equations intersect the y-axis.

May 7th, 2015

y = x + 10

y = -x + 3

Add the 2 equations to eliminate x

2y = 13

y = 13/2

y = 6.5


Substitute y in the first equation

6.5 = x + 10

x = 6.5 - 10

x = -3.5


ANSWER:  Add the equations to eliminate x.

May 7th, 2015

Thank you. Do you have time time to do one more question?

May 7th, 2015

Ok.

May 7th, 2015

A matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. Which of the following options represents the number of children and the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers?

A: 7 children and 28 adultsEquation 1: a + c = 35Equation 2: 6a − c = 70

B: 7 children and 28 adultsEquation 1: a + c = 35Equation 2: 6a + c = 70

C: 28 children and 7 adultsEquation 1: a + c = 35Equation 2: 6a + c = 70

D: 28 children and 7 adultsEquation 1: a + c = 35Equation 2: 6a − c = 70


May 7th, 2015

Total number of adults = a

total number of children = c

Cost of a matinee ticket for adult = $6

Cost of a matinee ticket for child = $1


The total number of adults (a) and children (c) who saw a movie was 35

a + c = 35


The total money collected was $70

6a + c = 70


So we have got the 2 equations 

a + c = 35  ----(1)

6a + c = 70 ----(2)


Now you should try solving these equations on your own. If you have any doubt I will help you out.

Hint - Subtract eqaution (1) from equation (2) to eliminate c .

May 7th, 2015

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May 7th, 2015

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