Question

Solve the simultaneous equations

2x + 4y = 1
3x - 5y = 7
y=1.5 x=
What does x equal

Answer 1

The solution to the system of equations be:

x = 0.5, y = -0.5

Explanation:

Given the system of equations

`\begin{bmatrix}2x+4y=1\\ 3x-5y=7\end{bmatrix}`

Multiply 2x+4y=1 by 3: 6x+12y=3

Multiply 3x-5y=7 by 2: 6x-10y=14

`\begin{bmatrix}6x+12y=3\\ 6x-10y=14\end{bmatrix}`

subtracting the equations

`6x-10y=14`

`-`

`\underline{6x+12y=3}`

`-22y=11`

solve -22y for y

`-22y=11`

Divide both sides by -22

`(-22y)/(-22)=(11)/(-22)`

Simplify

`y=-(1)/(2)`

`y = -0.5`

For 6x+12y=3 plug in y = -1/2

`6x+12\left(-(1)/(2)\right)=3`

`6x-12\cdot (1)/(2)=3`

`6x-6=3`

Add 6 to both sides

`6x-6+6=3+6`

`(6x)/(6)=(9)/(6)`

Simplification

`x=(3)/(2)`

`x = 1.5`

Therefore, the solution to the system of equations be:

x = 0.5, y = -0.5