Pergunta

Solve using substitution. 7x+8y=-9 5x-4y=13 d square
Solução

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BentoVeterano · Tutor por 10 anos
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To solve the system of equations using substitution, we can solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation for x:
7x + 8y = -9
7x = -9 - 8y
x = \frac{-9 - 8y}{7}
Now, substitute this expression for x into the second equation:
5x - 4y = 13
5\left(\frac{-9 - 8y}{7}\right) - 4y = 13
\frac{-45 - 40y}{7} - 4y = 13
-45 - 40y - 28y = 91
-68y = 136
y = -2
Now that we have the value of y, we can substitute it back into the expression for x:
x = \frac{-9 - 8(-2)}{7}
x = \frac{-9 + 16}{7}
x = \frac{7}{7}
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -2.
Let's solve the first equation for x:
7x + 8y = -9
7x = -9 - 8y
x = \frac{-9 - 8y}{7}
Now, substitute this expression for x into the second equation:
5x - 4y = 13
5\left(\frac{-9 - 8y}{7}\right) - 4y = 13
\frac{-45 - 40y}{7} - 4y = 13
-45 - 40y - 28y = 91
-68y = 136
y = -2
Now that we have the value of y, we can substitute it back into the expression for x:
x = \frac{-9 - 8(-2)}{7}
x = \frac{-9 + 16}{7}
x = \frac{7}{7}
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -2.
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