"Is (1,1) a solution to this system of equations? 4x + 10y = 14 x + 6y = 7 Choices: [[yes][no]] "

Substitute and check first equation: Substitute the point (1,1) into the first equation, 4x + 10y = 14, to check if it holds true. Substituting x=1 and y=1 gives us 4(1) + 10(1). Calculate first equation: Perform the calculation for the first equation: 4(1) + 10(1) = 4 + 10 = 14, which matches the right side of the equation, so the point (1,1) satisfies the first equation. Substitute and check second equation: Substitute the point (1,1) into the second equation, x + 6y = 7, to check if it holds true. Substituting x=1 and y=1 gives us 1(1) + 6(1). Calculate second equation: Perform the calculation for the second equation: 1(1) + 6(1) = 1 + 6 = 7, which matches the right side of the equation, so the point (1,1) satisfies the second equation as well. Conclusion: Since the point (1,1) satisfies both the first and the second equations, we can conclude that (1,1) is indeed a solution to the system of equations.

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Is $(1,1)$ a solution to this system of equations? $\newline$ $4x + 10y = 14$ $\newline$ $x + 6y = 7$ $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Algebra 2

Is (x, y) a solution to the system of equations?

Full solution

Q. Is

(1,1)

a solution to this system of equations?

\newline

4x + 10y = 14

\newline

x + 6y = 7

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Substitute and check first equation: Substitute the point $(1,1)$ into the first equation, $4x + 10y = 14$ , to check if it holds true. Substituting $x=1$ and $y=1$ gives us $4(1) + 10(1)$ .
Calculate first equation: Perform the calculation for the first equation: $4(1) + 10(1) = 4 + 10 = 14$ , which matches the right side of the equation, so the point $(1,1)$ satisfies the first equation.
Substitute and check second equation: Substitute the point $(1,1)$ into the second equation, $x + 6y = 7$ , to check if it holds true. Substituting $x=1$ and $y=1$ gives us $1(1) + 6(1)$ .
Calculate second equation: Perform the calculation for the second equation: $1(1) + 6(1) = 1 + 6 = 7$ , which matches the right side of the equation, so the point $(1,1)$ satisfies the second equation as well.
Conclusion: Since the point $(1,1)$ satisfies both the first and the second equations, we can conclude that $(1,1)$ is indeed a solution to the system of equations.