Question

Solve the simultaneous equation -4x+3y=1 6x-y=2

Answer 1

Answer:

x = 1/2, y = 1

Step-by-step explanation:

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer 2

Answer:

x = ¹/₂

y = 1

Step-by-step explanation:

Given system of equations:

$\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}$

Multiply the second equation by 3:

$\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2$

$\implies 18x-3y=6$

Add this to the first equation to eliminate the term in y:

$\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}$

Solve for x:

$\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}$

Substitute the found value of x into the first equation and solve for y:

$\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}$

Therefore, the solution to the given system of equations is:

x = ¹/₂ and y = 1

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