Question

solve the following system of equations using the elimination method.
$5x + 3y = 1$
$x + 2y = 3$
a $(-1, 2)$
b $(-1, -2)$
c $(1, -2)$
d $(1, 2)$

Explanation:

Step1: Multiply second equation by 5

$5(x + 2y) = 5 \times 3$
$5x + 10y = 15$

Step2: Subtract first equation from new equation

$(5x + 10y) - (5x + 3y) = 15 - 1$
$7y = 14$

Step3: Solve for y

$y = \frac{14}{7} = 2$

Step4: Substitute y=2 into second equation

$x + 2(2) = 3$
$x + 4 = 3$

Step5: Solve for x

$x = 3 - 4 = -1$

Answer:

A. $(-1, 2)$