Question

consider the system of equations. graph it
$5x + y = 9$
$10x - 7y = -18$
what is the solution to the system of equations?
a $(1, 4)$
b $(4, -8)$
c $(2.1, -1.5)$
d $(4, -11)$

Explanation:

Step1: Isolate $y$ from first equation

From $5x + y = 9$, rearrange to get:
$y = 9 - 5x$

Step2: Substitute $y$ into second equation

Substitute $y = 9 - 5x$ into $10x - 7y = -18$:
$10x - 7(9 - 5x) = -18$

Step3: Expand and simplify for $x$

Expand and combine like terms:
$10x - 63 + 35x = -18$
$45x - 63 = -18$
$45x = -18 + 63$
$45x = 45$
$x = \frac{45}{45} = 1$

Step4: Calculate $y$ with $x=1$

Substitute $x=1$ into $y = 9 - 5x$:
$y = 9 - 5(1) = 4$

Answer:

A. (1, 4)