Property 5
First Degree with Two Unknown Equation
Let \(a_1,a_2,b_1,b_2,c_1,c_2\) be non-zero real numbers;
\(a_1x+b_1y=c_1\)
\(a_2x+b_2y=c_2\)
The system consisting of two unknowns is called a system of equation with two unknowns. Generally the elimination method is used to find the solution of pair of values for x and y (x, y) In the elimination method, the coefficients of x or y in the system of equations are equalized with opposite signs, and one of the variables is eliminated by adding these equations on each side of the equal sign.
\(\begin{aligned}2x+3y&=18\\5x+2y&=23\end{aligned}\)
\(\begin{aligned}-2\,/\quad 2x+3y&=18\\3\,/\quad 5x+2y&=23\end{aligned}\)
\(\begin{array}{r}-4x-6y=-36\\+\quad15x+6y=69\\\hline11x=33\\x=3\end{array}\)
Then, the x value is inserted in any of the equations to find the y value.
\(\begin{aligned}2x+3y&=18\\2\cdot3+3y&=18\\3y&=12\\y&=4\\S.S.&=\{(3,4)\}\end{aligned}\)
1.
\(a-b=6\)
\(a+b=14\)
\(\Rightarrow a=?\)
2.
\(2a-b=12\)
\(a+b=3\)
\(\Rightarrow b=?\)
3.
\(2a+3b=17\)
\(a-b=1\)
\(\Rightarrow a=?\)
4.
\(3a-2b=11\)
\(2a+b=12\)
\(\Rightarrow b=?\)
5.
\(4x-3y=8\)
\(2x+4y=26\)
\(\Rightarrow x=?\)
6.
\(3x+2y=1\)
\(4x+3y=1\)
\(\Rightarrow x=?\)
7.
\(5x-3y=9\)
\(2x+2y=10\)
\(\Rightarrow x\cdot y=?\)
8.
\(\samefrac2x-\samefrac3y=0\)
\(\samefrac1x+\samefrac1y=5\)
\(\Rightarrow x=?\)
9.
\(\samefrac2x+\samefrac3y=12\)
\(\samefrac4x+\samefrac1y=9\)
\(\Rightarrow x=?\)
10.
\(\samefrac2x+\samefrac3y=2\)
\(\samefrac2x+\samefrac6y=3\)
\(\Rightarrow x=?\)