Audreykirsten08idn
Answered

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Use elimination method.
2x - y = 7
3x + 3y = 24​

Sagot :

TheoDidn

[tex]\mathbb{SOLUTION:}[/tex]

First, We need to start with the given system elimination to find x and y.

  • [tex]\begin{cases} 2x - y = 7 & \text{...(1)} \\ 3x + 3y = 24 & \text{...(2)} \end{cases}[/tex]

Multiply the first equation by 3.

  • [tex]\begin{cases} 3(2x - y = 7) & \text{...(1)} \\ 3x + 3y = 24 & \text{...(2)} \end{cases}[/tex]

Add the number by eliminating by x.

  • [tex]\begin{gathered} 6x - 3y = 21 \\ \cfrac{3x + 3y = 24}{9x + 0 = 45} \end{gathered}[/tex]

Then solve for x,

[tex]\quad\begin{gathered} 9x = 45 \\ x = \frac{45}{9} \\ x = 5\end{gathered}[/tex]

Solve for elimated variable using either or the original equations. So, we found the value of x, then let's plug it back in to solve for y.

[tex]\quad \quad \quad \quad \quad \quad \begin{gathered} 2x - y = 7 \\ 2(5) - y = 7 \\ 10 - y = 7 \\ y + -10 = 7 \\ y = 7 + -10 \\ y = -3 \\ \frac{y}{-1} = \frac{-3}{-1} \\ y = 3 \end{gathered}[/tex]

Hence, The solution is (5, 3)

Answer : [tex]\boxed{\rm (5, 3)}[/tex]

Spierreidn

PROBLEM

Use elimination method

2x - y = 7

3x + 3y = 24

Solution

[tex]1. \: 2x - y = 7 \\ 2. \: 3x + 3y = 24[/tex]

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is substracted from the other.

  • 2x - y = 7, 3x + 3y = 24

To make 2x and 3x equal multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2.

  • 3 × 2x + 3x(- 1) y = 3 × 7, 2 × 3x + 2 × 3y = 2 × 24
  • 6x - 3y = 21, 6x + 6y = 48

Substract 6x + 6y = 48 from 6x - 3y = 21 by substracting like terms on each side of the equal sign.

  • 6x - 6y - 3y - 6y = 21 - 48

Add 6x to -6x. Terms 6x and 6x cancel out, leaving an equation with only one variable that can be solved.

  • -3y - 6y = 21 - 48
  • 9y = 21 - 28
  • 9y = -27
  • y = 3

Subsititute 3 for y in 3x + 3y = 24, because the resulting equation contains only one variable, you can solve for x directly.

  • 3x + 3 × 3 = 24
  • 3x + 9 = 24
  • 3x = 15
  • x = 5

Therefore,

  • y = 3, x = 5