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In this lesson, we will learn how to solve a system of equations by substituting one equation into the other.

Q1:

Find π₯ given 2 π₯ β π¦ = 5 and π¦ = 7 π₯ .

Q2:

Solve the simultaneous equations π¦ + 4 π₯ = β 8 and π¦ = 5 π₯ + 1 0 .

Q3:

Solve the simultaneous equations 2 π₯ + π¦ = 1 1 and π₯ β 2 π¦ = 3 .

Q4:

Solve the simultaneous equations π₯ β π¦ = 4 and π₯ + π¦ = 1 4 .

Q5:

Shady and Maged each have a marble collection to sell. Maged has 1 more than 3 times the number of marbles Shady has. How many marbles does each boy have to sell if the total number of marbles is 113?

Q6:

Find two numbers whose sum is 28 and difference is 13.

Q7:

The difference between two numbers is 9. Twice the sum of the two numbers is 10. Find the two numbers.

Q8:

Solve the simultaneous equations π₯ + 4 π¦ = 1 7 and 2 π₯ + 7 π¦ = 5 .

Q9:

Find the values of π and π , given the arithmetic mean between π and π is 62 and the arithmetic mean between 2 π and 3 π is 3 2 1 2 .

Q10:

Find the values of π and π , given the arithmetic mean between π and π is β 3 4 and the arithmetic mean between 4 π and 2 π is β 7 6 .

Q11:

Find the values of π₯ and π¦ , given the arithmetic mean between π₯ and π¦ is 77.5 and the arithmetic mean between 7 π₯ and 6 π¦ is 467.

Q12:

If 7 π₯ β 4 π¦ = 8 and π₯ = 4 , what is the value of π¦ ?

Q13:

Given that ( β 2 π , 8 ) = ( 2 π β 2 , π ) , find the values of π and π .

Q14:

If π₯ + π¦ = 7 0 and π₯ = 4 7 , what is the value of π¦ ?

Q15:

Solve the simultaneous equations by first finding an equation in π₯ and then π¦ .

Q16:

If 7 π₯ β π¦ = 2 1 and π¦ = 4 π₯ , find π₯ .

Q17:

Solve the simultaneous equations by first finding an equation in terms of π₯ and then substituting your value of π₯ to find π¦ .

Q18:

Karimβs fatherβs age equals Karimβs age multiplied by 10. If difference between their ages is 18 years, how old are they?

Q19:

Two integers π₯ and π¦ have a sum of 82 and a product of 1 6 8 0 . Write an equation which could be solved to find the possible values of π₯ .

Q20:

Solve the following system of equations:

Q21:

Q22:

Two numbers have a sum of 56. If one number is one-third of the other, what are the numbers?

Q23:

A manβs age is 9 more than 2 times his sonβs age. Given that the sum of their ages is 57, find each of their ages.

Q24:

A movie theater sold 1 2 0 0 tickets. If a childβs ticket costs $5.95, an adultβs ticket costs $11.15, and the total revenue was $ 1 2 7 5 6 , how many of each type of ticket did they sell?

Q25:

Solve the simultaneous equations 2 π₯ β π¦ = 1 4 and 2 π¦ β 3 π₯ = 5 .

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