Question

change any one equation from given: 2y + x =9 and 3y-4x=8​

Answer 1

Answer:

How do you solve a pair of linear equations, 2y – x = 2 and 3 y -4x = -2?

x, y={2, 2}

PREMISES

2y-x=2 and 3y-4x=-2 [A system of two (2) linear equations]

ASSUMPTIONS

Let y=(x+2)/2

Let x=2y-2

CALCULATIONS

3(2y-x=2)–2(3y-4x=-2) [Multiply the coefficients of each equation by a factor such that one term in each equation will be the same. This change in the notation facilitates the elimination of one of the two variables in the system of equations and obtains a single equation in one variable]

(6y-3x=6)-(6y-8x=-4)

(6y-6y-3x+8x)=6-(-4)

0y+5x=6+4

5x=10

5x/5=10/5

x=2

and,

if y=(x+2)/2, then

y=(2+2)/2

y=4/2 and

y=2

hence,

x, y=

{2, 2}

PROOF

If x, y={2, 2}, then the system of two (2) linear equations

2y-x-3y+4x=2-(-2)

2(2)-2–3(2)+4(2)=2+2

4–2–6+8=2+2

2+2=2+2 and

4=4 establishes the roots (zeros) x, y={2, 2} of the system of linear equations 2y-x=2 and 3y-4x=-2

C.H.