Pergunta

What is the solution to the system of equations? ) -2x+3y=13 3x+4y=6 (-2,3) C (-(7)/(2),2) (3,-2) (-11,3)
Solução

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VascoElite · Tutor por 8 anos
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To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.<br /><br />First, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:<br /><br />$\begin{cases} -6x + 9y = 39\\ 6x + 8y = 12\end{cases}$<br /><br />Next, we can add the two equations together to eliminate x:<br /><br />$-6x + 9y + 6x + 8y = 39 + 12$<br /><br />$17y = 51$<br /><br />Dividing both sides by 17, we get:<br /><br />$y = 3$<br /><br />Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:<br /><br />$-2x + 3(3) = 13$<br /><br />$-2x + 9 = 13$<br /><br />Subtracting 9 from both sides, we get:<br /><br />$-2x = 4$<br /><br />Dividing both sides by -2, we get:<br /><br />$x = -2$<br /><br />Therefore, the solution to the system of equations is $(-2, 3)$.
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