Solutions of Simultaneous Linear Equations: Substitution Method

Q.

Solve $2x-y=5$ and $3x+2y=11$ by substitution.

Q.

$4$ men and $6$ women can finish work in $8$ days while $3$ men and $7$ women can do that same work in $10$ days. In how many days will $10$ women do the same work.

Q. When Seven times an even number is added to an odd number, it results in $21.$When the same even number is subtracted from thrice the odd number, $19$ is obtained. The sum of the numbers is .

Q. In a set of $216$ marbles, there are $x$ black marbles and $y$ white marbles. If the number of white marbles is $7$ times the number of black marbles, how many black marbles are there?

1. $56$
2. $27$
3. $32$
4. $189$

Q. When $2$ is added to the numerator of a fraction, $\frac{4}{5}$ is obtained. Whereas when $2$ is subtracted from the denominator of the fraction, $\frac{2}{3}$ is obtained. Comment on the type of fraction.

1. The fraction is a proper fraction.
2. The fraction is an improper fraction.
3. There exist no such fractions.

Q. Carolina is mowing lawns for a summer job. For every lawn mowed, she charges a fixed amount plus $\$6$ for each hour of work. Her total fee for a $4-$hour job is $\$32$. Which of the following is the correct slope-intercept equation for the given situation?

1. $6y=4x+32$
2. $y=6x+8$
3. $y=4x+6$
4. $32y=6x+4$

Q. The sum of two numbers is $25.$ One of the numbers exceeds the other by $5.$ Find the numbers.

1. $16$ and $9$
2. $10$ and $15$
3. $12$ and $17$
4. $20$ and $5$

Q.

A sand dune stands $5\text{feet}$ above sea level. The hill is eroding at a rate of $1\text{foot}$ per $20\text{years}$. Let $y$ represent the height of the sand dune after $x\text{years}$. Which equation represents the situation?

Q.

For two simultaeous linear equations with two variables, say $x$ and $y,$ arrange the given steps in proper order to find solution of the equations using substitution.

Step a: Solve the $2^{nd}$ equation to find $y.$

Step b: Substitute the value of $y$ in one of the given equations to obtain the value of $x.$

Step c: Inject/ substitute $x$ in the $2^{nd}$ equation to make it a linear equation in one variable.

Step d: In $1^{st}$ equation, solve for $x$ in terms of $y.$

1. $a\to b\to c\to d$
2. $d\to c\to a\to b$

Q. Find the solution for the following pair of equations
$3x-8y=4$
$x=2y$

1. $(-4,-2)$
2. $(2,1)$
3. $(0,-\frac{1}{2})$
4. $(0,0)$

Q. Find the solution for the following pair of equations
$4y-3x=-7$
$3x-2y=5$

1. $(-1,-4)$
2. $(3,2)$
3. $(2,\frac{1}{2})$
4. $(1,-1)$

Q.

Complete the following table and by inspection of the table find the solution of the equation $17-3y=5$.

$y$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$.....$
$17-3y$	$.....$	$.....$	$.....$	$.....$	$.....$	$.....$	$.....$	$.....$	$.....$	$.....$

Q. Solve the following simultaneous linear equations using the substitution method.
$5y=27x+8;100y-200x-704=0$

x-coordinate is

y-coordinate is

Q. Find the solution for the following pair of equations
$2x+y=2$
$x+2y=5$

1. $(-\frac{1}{3},\frac{8}{3})$
2. $(0,\frac{5}{2})$
3. $(0,2)$
4. $(1,0)$

Q.

Solve the system of equations.
$$\begin{gathered} 2x+y=3 \\ x=2y-1 \end{gathered}$$

Q. Choose the answer from the following:
Solve the given system of linear equations using the substitution method
$x=2y-1$
$x=y$

1. $(2,2)$
2. $(0,0)$
3. $(1,1)$
4. $(3,3)$

Q.

Solve the following equations by the substitution method :

$$\begin{gathered} \frac{x+11}{7}+2y=10 \\ 3x=8+\frac{y+7}{11} \end{gathered}$$

Q. Every morning, Michael goes for a jog. He noticed that he is losing weight, as estimated by the equation $y=mx-3$, where $y$ represents the weight loss in kilograms and $x$ represents the number of months. If he has lost $13$ kg in four months, what is the value of $m$?

1. $2$
2. $3$
3. $4$
4. $-4$

Q. Eleanor and Madison completed a work in 6 days. If the efficiency of Eleanor is twice that of Madison, find the part of work done by Madison.

1. ${\frac{1}{18}}^{th}$ part
2. ${\frac{1}{3}}^{th}$ part

Q. The solution for the following pair of equations
$y=2+5x$ and $y+3x=10$ is

1. $(2,12)$
2. $(0,10)$
3. $(3,1)$
4. $(1,7)$

Q.

Solve the following equations by the substitution method :

$$\begin{gathered} x=3y-19 \\ y=3x-23 \end{gathered}$$

Q. Find the solution for the following pair of equations
$2y+x=4$
$3y-\frac{1}{2}x=2$

1. $(1,2)$
2. $(2,1)$
3. $(0,2)$
4. $(2,3)$