Solve the system of equations by elimination :
6X - 9Y = 10
6X + 2Y = 18

hint Hint:

HINT: Perform any arithmetic operation and then find.

The correct answer is: x=91/33 and y=8/11

Complete step by step solution:
Let 6x - 9y = 10…(i)
and 6x + 2y = 18….(ii)
On subtracting (i) from (ii),
we get LHS to be 6x + 2y - (6x - 9y) = 2y - (- 9y) = 11y
and RHS to be 18 -10 = 8
On equating LHS and RHS, we have 11y = 8
$not stretchy rightwards double arrow y equals 8 over 11$
On substituting the value of y in (i), we get $6 x minus 9 cross times 8 over 11 equals 10$
$not stretchy rightwards double arrow 6 x minus 72 over 11 equals 10$
$not stretchy rightwards double arrow 6 x equals 10 plus 72 over 11$
$not stretchy rightwards double arrow 6 x equals 182 over 11$
$not stretchy rightwards double arrow x equals 91 over 33$
Hence we get $x equals 91 over 33 text and end text y equals 8 over 11$
Note: We can also solve these system of equations by making the coefficients of
y to be the same in both the equations.

Use Substitution to solve each system of equations :
Y = 2X - 7
9X + Y = 15

Finding the answer to the given linear equation is the act of solving a linear equation. One of the algebraic techniques for solving a system of two-variable linear equations is the substitution approach. As the name suggests, the replacement method involves substituting a variable's value into a second equation. As a result, two linear equations are combined into one linear equation with just one variable, making it simple to solve. As an illustration, let us swap the value of the x-variable from the second equation and the y-variable from the first equation. By solving the problem, we can determine the value of the y-variable. Last but not least, we can solve any of the preceding equations by substituting the value of y. This procedure can easily be switched around so that we first solve for x before moving on to solve for y.