‘Linear Equations’ is an important topic for SSC exams. Generally, application-based questions of two variables are asked in the exams. The standard form of a two-variable linear equation is ax+by+c = 0 where x & y are two variables and a & b are not equal to zero. Only one linear equation of two variables cannot be solved without extra information or other equations. There are mainly four methods (Elimination, Substitution, Cross multiplication, and Determinant) of solving a two-variable based linear equation. From these four methods, mostly two methods (Elimination and Substitution) are used for solving which are given below with the help of examples.
Q) If 2x+3y-19 = 0 and x+7y-26 = 0, then find out the value of ‘y’.
Sol. 2x+3y-19 = 0 Eq.(i)
x+7y-26 = 0 Eq.(ii)
Here we will apply the Elimination method to get the values of the given variables.
In the elimination method, we need to equal the coefficient of either x or y to get the values. So for equating the coefficients of x, we need to multiply Eq.(i) by 1 and Eq.(ii) by 2.
2x+3y-19 = 0 Eq.(iii)
2x+14y-52 = 0 Eq.(iv)
Now equating Eq.(iii) and Eq.(iv)
2x+3y-19 = 2x+14y-52
14y-3y = 52-19
11y = 33
y = 3
Q) If 7x+2y = 74 and 5x-4y = 4, then find out the value of (x+y).
Sol. 7x+2y = 74 Eq.(i)
5x-4y = 4 Eq.(ii)
Here we will apply the Substitution method to get the values of the given variables.
In the substitution method, we need to substitute the variable from one equation with the help of another equation.
Take Eq.(i).
7x+2y = 74
2y = 74-7x Eq.(iii)
Now put Eq.(iii) in Eq.(ii).
5x-2(74-7x) = 4
5x-148+14x = 4
19x = 148+4 = 152
x = 8
Put the value x in Eq.(iii).
2y = 74-56
2y = 18
y = 9
value of (x+y) = 8+9 = 17
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