Question

Solve the system of equations 4x - 2y =8 3x + 4y = 17​

Answer 1

Answer:

x = 3 & y = 2

Step-by-step explanation:

$4x-2y=8;3x+4y=17$

$4x=2y+8$

$\frac{4x}{4} =\frac{2y+8}{4}$

$x=\frac{1}{2} y+2$

$3x+4y=17$

$3(\frac{1}{2} y+2)+4y=17$

$\frac{11}{2} y+6=17$

$\frac{11}{2} y+6+-6=17+-6$

$\frac{11}{2} y=11$

$\div2$

$y=2$

$x=\frac{1}{2} y+2$

$x=\frac{1}{2} (2)+2$

$x=3$

Hope this helps.

Answer 2

Answer:

Solution: x = 3, y = 2, or (3, 2)

Step-by-step explanation:

Given the systems of linear equations with two variables:  

$\displaystyle\mathsf{\left \{{Equation\:1:\:4x - 2y =\:8} \atop {Equation\:2:\:3x + 4y = 17}} \right}$

The process of elimination will be used to solve for the solution to the given problem.  

Step 1:

First, we must multiply Equation 1 by 2:

(2)[4x - 2y] = 8(2)

8x - 4y = 16

Step 2:

Add the revised Equation 1 (from the previous step) to Equation 2:

$\displaystyle\mathsf{\left \ {{\quad \:\:\:8x\:- 4y = 16} \atop + {\quad\underline {\:\:3x\:+ 4y = 17\:} \underline}} \right.}\\\displaystyle\mathsf{\qquad\:\:11x\qquad\:=33}$

Step 3:

Next, divide both sides by 11 to solve for x:

$\displaystyle\mathsf{\frac{11x}{11}\:=\:\frac{33}{11}}$

x = 3

Step 4:

Substitute the value of x = 3 into Equation 1 to solve for y:

4x - 2y = 8

4(3) - 2y = 8

12 - 2y = 8

Step 5:

Subtract 12 from both sides:

12 - 12 - 2y = 8 - 12

- 2y = -4

Step 6:

Divide both sides by -2 to solve for y:

$\displaystyle\mathsf{\frac{-2y}{-2}\:=\:\frac{-4}{-2} }$

y = 2

Double-check:

In order to verify whether we have the correct values for the solution, substitute x = 3, and y = 2 into both equations:

Equation 1:  4x - 2y = 8  

4(3) - 2(2) = 8  

12 - 4 = 8

8 = 8 (True statement).

Equation 2: 3x + 4y = 17​

3(3) + 4(2) = 17​

9 + 8 = 17

17 = 17 (True statement).

Therefore, the solution to the given system is x = 3, y = 2, or (3, 2).