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GB-20-01-001 · Linear elimination

Solve the simultaneous equations
4x+y=−144x+y=-14
9x−y=−389x-y=-38

Simultaneous Equations: Linear (Elimination) 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-20-01-001)
1)
Label the equations: 4x+1y=−14(1)4x + 1y=-14\quad(1) and 9x−1y=−38(2)9x - 1y=-38\quad(2).
2)
Match the first-letter coefficients: (1) × 9, (2) × 4.
3)
36x+9y=−12636x−4y=−152(9−(−4))y=−126−(−152)\begin{array}{rcl}36x + 9y&=&-126\\ 36x - 4y&=&-152\\\hline (9-(-4))y&=&-126-(-152)\end{array}
4)
Subtract the entire second equation, including its signs: 13y=26⇒y=213y=26\Rightarrow y=2.
5)
Substitute into (1): 4x+(1)(2)=−14⇒4x=−16⇒x=−44x+(1)(2)=-14\Rightarrow 4x=-16\Rightarrow x=-4.
Ans = x=−4,  y=2x=-4,\;y=2