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Solve the system of equations using elimination:
2x+3y=-14 and
x+5y=0.

Solve the system of equations using elimination: $2 x+3 y=-14$ and $x+5 y=0$ .

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Solve a system of equations in three variables using elimination

Full solution

Q. Solve the system of equations using elimination:

2 x+3 y=-14

and

x+5 y=0

.

Write Equations: Write down the system of equations. $\newline$ $2x + 3y = -14$ $\newline$ $x + 5y = 0$
Multiply and Set Up: Multiply the second equation by $-2$ to set up for elimination of $x$ . $-2(x + 5y) = -2(0)$ $-2x - 10y = 0$
Eliminate x: Add the modified second equation to the first equation to eliminate x. $\newline$ $(2x + 3y) + (-2x - 10y) = -14 + 0$ $\newline$ $2x - 2x + 3y - 10y = -14$ $\newline$ $0x - 7y = -14$
Solve for y: Solve for y. $\newline$ $-7y = -14$ $\newline$ $y = \frac{-14}{-7}$ $\newline$ $y = 2$
Substitute and Find $x$ : Substitute $y = 2$ into the second original equation to find $x$ . $x + 5(2) = 0$ $x + 10 = 0$ $x = -10$
Write Ordered Pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-10, 2)$ .

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