IGCSE Math B 3.H Linear simultaneous equations Topic Practice

Solution of linear simultaneous equations in two unknowns Simple questions may be set requiring the graphical solution of simultaneous linear equations

Solve the simultaneous equations
$\begin{aligned} 2x+3y&=2.5\\ 4x+2y&=7 \end{aligned}$

Show clear algebraic working.

[Maximum number: 4]

Solve the simultaneous equations
$\begin{aligned}3x+5y&=7.5\\7x+6y&=3.9\end{aligned}$
Show clear algebraic working.

[Maximum number: 4]

Solve the simultaneous equations
$\begin{aligned}3x-4y&=3\\4x-7y&=2\end{aligned}$
Show clear algebraic working.

[Maximum number: 4]

Solve the simultaneous equations

\begin{aligned} & 3 y=2-2 x \\ & 5 y=8-3 x \end{aligned}

[Maximum number: 3]

A mixture for concrete is made up of 105 kg of cement, 252 kg of sand and 273 kg of gravel.
Given that
$\text{cement} : \text{sand} : \text{gravel}=1:(2x+y):(x+2y).$

Hence solve these two equations for the value of x and for the value of y.
Give each value as a simplified fraction.

Solve the simultaneous equations
4x+4y=184x+6y=35.
Show clear algebraic working.
$x=\qquad y=$

[Maximum number: 6]

Figure 1 shows a kite ABCD where AB=BC.
$AB=(6x+2y-10)\text{ cm},\quad BC=(3x+y+1)\text{ cm},\quad AD=(2x+9y-14)\text{ cm},\quad CD=(5x+5y-9)\text{ cm}.$
Calculate the length, in cm, of the perimeter of the kite.

Solve the simultaneous equations

\begin{aligned} & 9 x+7 y=3 \\ & 5 x-4 y=6.4 \end{aligned}

Show clear algebraic working.

\begin{aligned} & x= \\ & y= \end{aligned}

Solve the simultaneous equations

\begin{aligned} 2 x-3 y & =8 \\ \frac{y}{2} & =x-3 \end{aligned}

Show clear algebraic working.

\begin{aligned} & x=\ldots \\ & y=\ldots \end{aligned}

Solve the simultaneous equations
$\begin{cases} 3x+2y=8,\\ -4x+9y=22. \end{cases}$
Show clear algebraic working.

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Question 1

Question 1

Question 1

Question 2

Question 2(b)

Question 5

Question 2

Question 15

Question 12

Question 14