Question

on your own
solve the system of linear equations by elimination. check
your solution.

1. $3x + y = 11$

$6x + 3y = 24$

1. $4x - 5y = -19$

$-x - 2y = 8$

1. $5y = 15 - 5x$

$y = -2x + 3$

Explanation:

Problem 4

Step1: Multiply first equation by 3

Multiply $3x + y = 11$ by 3:
$3(3x + y) = 3\times11$
$9x + 3y = 33$

Step2: Subtract second equation

Subtract $6x + 3y = 24$ from the new equation:
$(9x + 3y) - (6x + 3y) = 33 - 24$
$3x = 9$

Step3: Solve for x

$\frac{3x}{3} = \frac{9}{3}$
$x = 3$

Step4: Substitute x into first equation

Plug $x=3$ into $3x + y = 11$:
$3(3) + y = 11$
$9 + y = 11$

Step5: Solve for y

$y = 11 - 9$
$y = 2$

Step6: Check solution

Substitute $x=3, y=2$ into $6x + 3y = 24$:
$6(3) + 3(2) = 18 + 6 = 24$, which matches.

Step1: Multiply second equation by 4

Multiply $-x - 2y = 8$ by 4:
$4(-x - 2y) = 4\times8$
$-4x - 8y = 32$

Step2: Add to first equation

Add to $4x - 5y = -19$:
$(4x - 5y) + (-4x - 8y) = -19 + 32$
$-13y = 13$

Step3: Solve for y

$\frac{-13y}{-13} = \frac{13}{-13}$
$y = -1$

Step4: Substitute y into second equation

Plug $y=-1$ into $-x - 2y = 8$:
$-x - 2(-1) = 8$
$-x + 2 = 8$

Step5: Solve for x

$-x = 8 - 2$
$-x = 6$
$x = -6$

Step6: Check solution

Substitute $x=-6, y=-1$ into $4x - 5y = -19$:
$4(-6) - 5(-1) = -24 + 5 = -19$, which matches.

Step1: Rewrite first equation

Simplify $5y = 15 - 5x$ by dividing by 5:
$y = 3 - x$

Step2: Set equations equal

Set $y = 3 - x$ equal to $y = -2x + 3$:
$3 - x = -2x + 3$

Step3: Solve for x

$-x + 2x = 3 - 3$
$x = 0$

Step4: Substitute x into second equation

Plug $x=0$ into $y = -2x + 3$:
$y = -2(0) + 3$
$y = 3$

Step5: Check solution

Substitute $x=0, y=3$ into $5y = 15 - 5x$:
$5(3) = 15 - 5(0)$
$15 = 15$, which matches.

Answer:

$x=3, y=2$

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Problem 5