QuestionFind the value of $5x - y$ given $x + y = 500$ and $3x + 2y = 3000$ .

Studdy Solution

STEP 1

Assumptions1. The system of equations is given as - $x+y=500$ - $3x+y=3000$ . We need to find the value of $5x-y$ .

STEP 2

We can solve this system of equations using substitution or elimination method. Here, we will use the elimination method. First, we will multiply the first equation by2 and the second equation by1 to make the coefficients of $y$ in both equations the same.
$2(x+y)=2(500)$ $x+2y=3000$

STEP 3

implify the equations.
$2x+2y=1000$ $3x+2y=3000$

STEP 4

Subtract the first equation from the second one to eliminate $y$ .
$(3x+2y)-(2x+2y)=3000-1000$

STEP 5

implify the equation to find the value of $x$ .
$x=2000$

STEP 6

Substitute $x=2000$ into the first equation to find the value of $y$ .
$2000+y=500$

STEP 7

olve the equation to find the value of $y$ .
$y=500-2000$ $y=-1500$

STEP 8

Substitute $x=2000$ and $y=-1500$ into the expression $5x-y$ to find its value.
$5x-y=5(2000)-(-1500)$

STEP 9

implify the expression to find the value of $5x-y$ .
$5x-y=10000+150$ $5x-y=11500$ The value of $5x-y$ is11500.

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