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Solve using elimination. $\newline$ $7x + 8y = 1$ $\newline$ $7x + 6y = 13$ $\newline$ (_, _)

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Solve a system of equations using elimination

Full solution

Q. Solve using elimination.

\newline

7x + 8y = 1

\newline

7x + 6y = 13

\newline

(_____, _____)

Identify Variables: System of equations: $\newline$ $7x + 8y = 1$ $\newline$ $7x + 6y = 13$ $\newline$ Which variable should we eliminate? $\newline$ Since the coefficient of $x$ is the same in both equations, we will eliminate $x$ .
Eliminate Variable: System of equations: $\newline$ $7x + 8y = 1$ $\newline$ $7x + 6y = 13$ $\newline$ Which operation should we use to eliminate $x$ ? $\newline$ Coefficients of $x$ : $7$ and $7$ $\newline$ Here the coefficients are the same, we should subtract the second equation from the first.
Subtract Equations: System of equations: $\newline$ $7x + 8y = 1$ $\newline$ $7x + 6y = 13$ $\newline$ Subtract the second equation from the first to eliminate $x$ . $\newline$ $(7x + 8y) - (7x + 6y) = 1 - 13$ $\newline$ $7x + 8y - 7x - 6y = -12$ $\newline$ $8y - 6y = -12$ $\newline$ $2y = -12$
Solve for y: $2y = -12$ $\newline$ Solve for y. $\newline$ Divide both sides of the equation by $2$ . $\newline$ $(2y) / 2 = -12 / 2$ $\newline$ $y = -6$
Substitute and Solve: Substitute $y = -6$ in $7x + 8y = 1$ .
$7x + 8(-6) = 1$
Solve for $x$ .
$7x - 48 = 1$
$7x = 1 + 48$
$7x = 49$
Final Solution: $7x = 49$ $\newline$ Solve for $x$ . $\newline$ Divide both sides of the equation by $7$ . $\newline$ $(7x) / 7 = 49 / 7$ $\newline$ $x = 7$
Final Solution: $7x = 49$ Solve for $x$ . Divide both sides of the equation by $7$ . $(7x) / 7 = 49 / 7$ $x = 7$ We found: $x = 7$ $y = -6$ Write the solution as a coordinate point. Solution: $(7, -6)$

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