Question

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If the system has one solution, find the solution.

Answer 1

The given system of equations has only one solution

The solution is (x, y) = (-1, 0)

Solution:

Given system of equations are:

-7x - 2y = 7 ---- eqn 1

4x + 6y = -4 --- eqn 2

We have to find solution for this system of equations by substitution method

From eqn 2,

4x + 6y = -4

2x + 3y = -2

2x = -2 - 3y

$x = -1 - \frac{3y}{2}$ --- eqn 3

Substitute eqn 3 in eqn 1

$-7(-1 - \frac{3y}{2}) - 2y = 7\\\\7 + \frac{21y}{2} - 2y = 7\\\\\frac{14 + 21y -4y}{2} = 7\\\\14 + 21y - 4y = 14\\\\17y + 14 = 14\\\\17y = 14 - 14\\\\17y = 0\\\\y = 0$

y = 0

Substitute y = 0 in eqn 1

-7x -2(0) = 7

-7x = 7

x = -1

Thus the solution is (x, y) = (-1, 0)

Therefore the given system of equations has only one solution