Henrique began to solve a system of linear equations using the linear combination method. His work is shown below:

Question

3(4x – 7y = 28) → 12x – 21y = 84
–2(6x – 5y = 31) → –12x + 10y = –62
12x – 21y = 84
+ –12x + 10y = –62
–11y = 22
y = –2
Complete the steps used to solve a system of linear equations by substituting the value of y into one of the original equations to find the value of x.

What is the solution to the system?

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Answer 1

To find the value of \( x \) after determining \( y = -2 \), we can substitute \( y \) back into one of the original equations. Let’s use the first equation from the system:

\[ 4x - 7y = 28 \]

Substituting \( y = -2 \):

\[ 4x - 7(-2) = 28 \] \[ 4x + 14 = 28 \] \[ 4x = 28 - 14 \] \[ 4x = 14 \] \[ x = \frac{14}{4} = \frac{7}{2} = 3.5 \]

Thus, the solution to the system of equations is:

\[ \left( \frac{7}{2}, -2 \right) \quad \text{or} \quad (3.5, -2) \]

So the final answer is:

\[ \left( 3.5, -2 \right) \]