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GB-20-03-001 · Simultaneous equations in context

Three sandwiches and two drinks cost £7.20. Two sandwiches and three drinks cost £7.80. Work out the cost of one sandwich and one drink.

Simultaneous Equations: Forming & Solving in Context Booklet p. 27
Method
1) Label both equations
2) Make the first-letter coefficients equal
3) Subtract the entire second equation, watching touching signs
4) Solve for the second letter
5) Substitute back to find the first
Worked Example (GB-20-03-001)
1)
Let x be the sandwich price and y the drink price, in pounds.
2)
Label the equations: 3x+2y=7.2(1)3x + 2y=7.2\quad(1) and 2x+3y=7.8(2)2x + 3y=7.8\quad(2).
3)
Match the first-letter coefficients: (1) × 2, (2) × 3.
4)
6x+4y=14.46x+9y=23.4(4−(9))y=14.4−(23.4)\begin{array}{rcl}6x + 4y&=&14.4\\ 6x + 9y&=&23.4\\\hline (4-(9))y&=&14.4-(23.4)\end{array}
5)
Subtract the entire second equation, including its signs: −5y=−9⇒y=1.8-5y=-9\Rightarrow y=1.8.
6)
Substitute into (1): 3x+(2)(1.8)=7.2⇒3x=3.6⇒x=1.23x+(2)(1.8)=7.2\Rightarrow 3x=3.6\Rightarrow x=1.2.
Ans = Sandwich £1.20; drink £1.80