Watch me solve a 2 Variable LINEAR SYSTEM - Can You Solve This Algebra Problem?

[@tomtke7351]

collect 'like' items... apples and oranges or "x's" and "y's." 2(x-y)=3x-1 2x-3x-2y=-1 -x-2y=-1 x+2y=1 eq.1 4y-3=-4-3x 3x+4y=-4+3 3x+4y=-1 eq.2 x+2y=1 eq.1 3x+4y=-1 eq.2 take eq.1 & × 3 3×{x+2y=1} 3x+6y=3 eq.1.1 subtract eq.2 from eq.1.1 3x+6y=3 eq.1.1 3x+4y=-1 eq.2 _______________________ 0x+2y =4 y=2 sol.1 from x+2y=1 eq.1 x+2(2)=1 x=1-4 x=-3 sol.2 VERIFY x=-3, y=2 3x+4y=-1 eq.2 3(-3)+4(2)=?-1 -9+8=❤-1✔️

[@panlomito]

Or watch me... First equation: 2x - 2y - 3x + 1 = 0 or x = 1 - 2y Second equation: 4y - 3 + 4 + 3x = 0 or 4y + 1 + 3 . (1 - 2y) = 0 so 4y + 1 + 3 - 6y = 0 4 = 2y so y = 2 and x = 1 - 2 . (2) = - 3 Check: 4 . (2) + 1 + 3 . (-3) = 8 + 1 - 9 = 0

[@Perseverance777]

Merry Christmas!

[@Stylux-z1p]

well... let see... Elimination Method: 2(x - y) = 3x - 1 --> Rearrange the 1st Equation 2x - 2y = 3x - 1 2x - 3x - 2y = -1 -x - 2y = -1 ------------------------------ 4y - 3 = -4 - 3x --> Rearrange the 2nd Equation 4y + 3x = -4 + 3 4y + 3x = -1 ---------------------------- -x - 2y = -1 --> flip the terms -x and 2y 4y + 3x = -1 so that the like terms align with terms of the 2nd equation -------------------------- [-2y - x = -1] * 2 ( multiply with 2 to eliminate the y variable) 4y + 3x = -1 -------------------------- -4y - 2x = -2 4y +3x = -1 (add the terms and constants) ------------------ x = -3✅ ---------------------------------- lets find the value of y by substituting the value of x = -3 in one of the equations 4y + 3x = -1 4y + 3[-3] = -1 4y - 9 = -1 4y = -1 +9 4y = 8 4y/4 = 8/4 y = 2✅ Solution to the 2-variable linear equation system: {-3, 2}✅✅ --------------------------------------------------------------- proof: 2(x - y) = 3x - 1 ---> 1st equation 2(-3 - 2) = 3(-3) - 1 2(-5) = -9 -1 -10 = -10✅ ------------------------- 4y - 3 = -4 - 3x 4(2) -3 = -4 - 3(-3) 8 - 3 = -4 + 9 5 = 5✅

[@robertstuart6645]

Excellent method and procedure for solving.

[@russelllomando8460]

got X = -3, Y = 2 isolate and substitute X = 1 - 2Y so 4Y - 3 = - 4 - 3 (1 - 2Y) lengthy but fun. thanks

[@chrisdissanayake6979]

Answer: X = -3 Y = 2 ------- 2(X-Y)=3X-1 4Y-3=-4-3X 2X-2Y=3X-1 --(1) 3X+4Y=-1. --(2) Multiplying equation (1) by 2, 4X-4Y=6X-2----(3) Adding equations (2) & (3), 7X=6X - 3 X= -3 Substituting X=-3 to equation (2), 3X+4Y=-1 -9+4Y=-1 4Y= 9-1=8 Y=2

[@KW-gb9cd]

(x, y) = (-3, 2).

[@stevendebettencourt7651]

Oh, this is gonna be fun. Let’s do this! 2(x - y) = 3x - 1 & 4y - 3 = -4 - 3x First, let’s get rid of any parentheses: 2x - 2y = 3x - 1 & 4y - 3 = -4 - 3x Looking at the first equation, let’s solve for x in terms of y: 3x - 1 = 2x - 2y x = 1 - 2y Now, putting this back into the first equation would not be helpful, so plug this into the second equation instead: 4y - 3 = -4 - 3x 4y - 3 = -4 - 3(1 - 2y) 4y - 3 = -4 - 3 + 6y 6y - 7 = 4y - 3 2y = 4 y = 2 Plugging this back into our equation for x: x = 1 - 2y x = 1 - 2(2) x = 1 - 4 x = -3 So we get x=-3 and y=2 as the solution. Just to be sure, let’s check the answer. 2(x - y) = 3x - 1 & 4y - 3 = -4 - 3x 2(-3 - 2) =? 3(-3) - 1 & 4(2) - 3 =? -4 - 3(-3) 2(-5) =? -9 - 1 & 8 - 3 =? -4 + 9 -10 =? -10 YES & 5 =? 5 YES Yay! Any questions?

[@josephlaura7387]

x= -3 y=2