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**Previous Year Questions - Pair of Linear Equations in Two Variables**
**Solve the following pair of linear equations:**
1. 3x + 4y = 10
2x - y = 1
**Solution:**
- **Step 1:**
Rearrange the equations to make y the subject in the second equation:
y = 2x - 1
- **Step 2:**
Substitute the value of y in the first equation:
3x + 4(2x - 1) = 10
3x + 8x - 4 = 10
11x = 14
x = 14/11
- **Step 3:**
Substitute the value of x in the second equation:
2(14/11) - y = 1
28/11 - y = 1
y = 28/11 - 1
y = 17/11
Therefore, the solution to the pair of linear equations is x = 14/11 and y = 17/11.
**Solve the following pair of linear equations using the substitution method:**
2. 3x - 5y = 7
2x + 3y = 1
**Solution:**
- **Step 1:**
Rearrange the equations to make x the subject in the first equation:
x = (5y + 7)/3
- **Step 2:**
Substitute the value of x in the second equation:
2((5y + 7)/3) + 3y = 1
(10y + 14)/3 + 3y = 1
10y + 14 + 9y = 3
19y = -11
y = -11/19
- **Step 3:**
Substitute the value of y in the first equation to find x:
x = (5(-11/19) + 7)/3
x = (-55/19 + 133/19)/3
x = 78/19
Therefore, the solution to the pair of linear equations is x = 78/19 and y = -11/19.