Question

2x-5y=4 , 3x-8y=5 cross multiplication

Answer 1

Answer:

2x-5y = 4 ----(1)

3x-8y = 5 ----(2)

(1)×3 = 6x-15y = 12 ----(3)

(2)×2 = 6x-16y = 10 ----(4)

Equation (4) - (3) = >> -y = -2

=>> y = 2

Substituting value of y in eq.(1)

2x-5(2) = 4

2x-10 = 4

2x = 4+10

2x = 14

x = 7

Answer 2

Answer:

$\Large\boxed{X=7, \quad Y=2}$

Step-by-step explanation:

Given:

2x-5y=4 , 3x-8y=5 (linear equation)

To solve this problem, first you have to solve with substitution of linear equation.

Solutions:

$\Large\boxed{\textnormal{LESSON: LINEAR EQUATIONS}}}$

First, you have to isolate by the x on one side of the equation.

$\displaystyle 2x-5y=4$

Add by 5y from both sides of an equation.

$\displaystyle 2x-5y+5y=4+5y$

Solve.

$\displaystyle 2x=4+5y$

Secondly, divide by 2 from both sides of an equation.

$\displaystyle \frac{2x}{2}=\frac{4}{2}+\frac{5y}{2}$

Solve.

$\displaystyle x=\frac{4+5y}{2}$

Solve with (substitute of x=4+5y/2.)

$\displaystyle 3* \frac{4+5y}{2}-8y=5$

Isolate by the y on one side of the equation.

Expand by using distributive property.

$\Large\boxed{\textnormal{DISTRIBUTIVE PROPERTY}}$

$\displaystyle A(B+C)=AB+AC$

$3* \frac{4+5y}{2}-8y=6-\frac{y}{2}$

$\displaystyle 6-\frac{y}{2}=5$

Then, multiply by 2 from both sides.

$\displaystyle 6*2-\frac{y}{2}*2=5*2$

Solve.

Multiply the numbers from left to right.

$\dipslaystyle 5*2=10$

$\displaystyle 12-y=10$

Subtract by 12 from both sides of an equation.

$\displaystyle 12-y-12=10-12$

Solve.

Add or subtract the numbers from left to right.

$\displaystyle 10-12=-2$

$\displaystyle -y=-2$

Divide by -1 from both sides of an equation.

$\displaystyle \frac{-y}{-1}=\frac{-2}{-1}$

Solve.

Divide the numbers from left to right.

$\displaystyle -2\div-1=\boxed{2}$

$\Large\boxed{Y=2}$

Solve with (substitute of 4+5y/2 and y=2.)

$\displaystyle \frac{4+5*2}{2}$

Used order of operations.

$\Large\boxed{\textnormal{ORDER OF OPERATIONS}}$

PEMDAS stands for (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract) the numbers from left to right.

First, multiply.

$\displaystyle 5*2=10$

Add.

$\displaystyle 10+4=14$

$\displaystyle 14\div2=\boxed{7}$

$\Large\boxed{X=7}$

$\Large\boxed{X=7, Y=2}$

Hence, the correct answer is y=2 and x=7.