Here is your answer.


3x - 5 = 4y. (1)

=3x -4y = 5

3y + 17 = 2+ 3x. (2)

= 3y -3x = -15

= x - y = 5
= x = 5 + y. [3]

putting this value of x in equation (1)
we get

3(5 + y) - 5 = 4y

15 + 3y -5 = 4y
15 - 5 = 4y - 3y

y = 10 [4]

putting the value of y in equation [3]

we get

x = 5 + y

x= 5 + 10 =15

therefore .{{ x = 15 and y = 10. }}

hope you got it

thanks

Linear Equations in Two Variables

Linear equations in two variables refer to the equations that have two variables and are of degree one. The general form of a linear equation in two variables is ax+by+c=0, where a, b, and c are constants. These equations can be solved graphically or algebraically.

Solving Linear Equations in Two Variables

To solve linear equations in two variables, we need to find the values of both variables that satisfy the equation. There are different methods to solve these equations, including substitution method, elimination method, and graphical method.

Example 1: 3x-15=4y

To solve the equation 3x-15=4y, we need to find the values of x and y that satisfy the equation. We can rewrite the equation in the form y=(3/4)x-15/4. This is the equation of a straight line in slope-intercept form, where the slope is 3/4 and the y-intercept is -15/4.

Example 2: 3y+17=23x

To solve the equation 3y+17=23x, we need to find the values of x and y that satisfy the equation. We can rewrite the equation in the form y=(23/3)x-17/3. This is the equation of a straight line in slope-intercept form, where the slope is 23/3 and the y-intercept is -17/3.

Example 3: 3y+17=2-3x

To solve the equation 3y+17=2-3x, we need to find the values of x and y that satisfy the equation. We can rewrite the equation in the form y=(-3/3)x-(17/3)-2/3, which simplifies to y=(-3/3)x-19/3. This is the equation of a straight line in slope-intercept form, where the slope is -1 and the y-intercept is -19/3.

Conclusion

Linear equations in two variables are important in mathematics and have many real-world applications. They can be solved using different methods, including substitution, elimination, and graphical methods. It is essential to understand the slope-intercept form of a straight line equation to solve these equations.