Chapter 4: Q. 70 (page 387)

Solve the system of equations by elimination and explain all your steps in words:
$\{\begin{cases} 5 x + 4 y = 10 \\ 2 x = 3 y + 27 \end{cases}$

Short Answer

Expert verified

The solution of system of system of linear equation $\{\begin{cases} 5 x + 4 y = 10 \\ 2 x = 3 y + 27 \end{cases}$ is $(6, - 5)$

Step by step solution

Given information and creating variable with same coefficient

Given equations:

$5 x + 4 y = 10 \dots . . (1) 2 x = 3 y + 27 \dots . . (2)$

Both equations are in standard form. So, elimination will work.

Multiply the first equation with $3 .$

$3 (5 x + 4 y) = 3 (10)$

Simplify parenthesis:

localid="1658851619517" $15 x + 12 y = 30 . . . . . (3)$

Multiply the second equation with $4$

localid="1658851625849" $\begin{matrix} 4 (2 x) = 4 (3 y + 27) \\ 8 x = 12 y + 108 \\ 8 x - 12 y = 108 . . . . (4) \end{matrix}$

solving for x and y

Solving equation $3$ and $4$

Adding equations 3 and 4 we get

$x = 138 \div 23$

$x = 6$

Substitute $x = 6$ in any one of the equations and solve for localid="1658851682925" $y$

Consider: $5 x + 4 y = 10$

Substitute:

$5 (6) + 4 y = 10$

Multiply:

$30 + 4 y = 10$

$4 y = - 20$

$y = - 20 \div 4$

$y = - 5$

Hence the solution is $(6, - 5)$

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Solve the system of equations by elimination and explain all your steps in words:
$\{\begin{cases} 5 x + 4 y = 10 \\ 2 x = 3 y + 27 \end{cases}$

Short Answer

Step by step solution

Given information and creating variable with same coefficient

solving for x and y

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Solve the system of equations by elimination and explain all your steps in words:5x+4y=102x=3y+27

Short Answer

Step by step solution

Given information and creating variable with same coefficient

solving for x and y

One App. One Place for Learning.

Most popular questions from this chapter

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Solve the system of equations by elimination and explain all your steps in words:
$\{\begin{cases} 5 x + 4 y = 10 \\ 2 x = 3 y + 27 \end{cases}$