Question

solve the following system using the elimination method.
$7x - 2y = 8$
$4x + 5y = -9.25$
$x = 0.5$
correct. good job!
$y = 2.25$
thats not it.
thats not it. try again. score: 50%

Explanation:

Step1: Eliminate $y$ by scaling equations

Multiply first eq by 5: $35x - 10y = 40$
Multiply second eq by 2: $8x + 10y = -18.5$

Step2: Add the two new equations

$35x - 10y + 8x + 10y = 40 + (-18.5)$
$43x = 21.5$

Step3: Solve for $x$

$x = \frac{21.5}{43} = 0.5$

Step4: Substitute $x=0.5$ into first equation

$7(0.5) - 2y = 8$
$3.5 - 2y = 8$

Step5: Solve for $y$

$-2y = 8 - 3.5$
$-2y = 4.5$
$y = \frac{4.5}{-2} = -2.25$

Answer:

$x=0.5$, $y=-2.25$