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Solve the system of equations:

[tex]\[
\begin{cases}
3x = 6 - 4y \\
16y - 21 = -12
\end{cases}
\][/tex]

Sagot :

GinnyAnsweridn
To solve the system of linear equations:

[tex]\[ \left\{ \begin{array}{l} 3x = 6 - 4y \\ 16y - 21 = -12 \end{array} \right. \][/tex]

we'll follow these steps:

1. Solve the second equation for [tex]\(y\)[/tex]:

[tex]\[ 16y - 21 = -12 \][/tex]

Add 21 to both sides to isolate the term with [tex]\(y\)[/tex]:

[tex]\[ 16y = -12 + 21 \][/tex]

Simplify the right side:

[tex]\[ 16y = 9 \][/tex]

Divide both sides by 16 to solve for [tex]\(y\)[/tex]:

[tex]\[ y = \frac{9}{16} \][/tex]

2. Substitute [tex]\(y\)[/tex] into the first equation to solve for [tex]\(x\)[/tex]:

The first equation is:

[tex]\[ 3x = 6 - 4y \][/tex]

Substitute [tex]\(y = \frac{9}{16}\)[/tex] into the equation:

[tex]\[ 3x = 6 - 4 \left(\frac{9}{16}\right) \][/tex]

Simplify the term involving [tex]\(y\)[/tex]:

[tex]\[ 3x = 6 - \frac{36}{16} \][/tex]

Simplify [tex]\(\frac{36}{16}\)[/tex]:

[tex]\[ 3x = 6 - 2.25 \][/tex]

Subtract 2.25 from 6:

[tex]\[ 3x = 3.75 \][/tex]

Divide both sides by 3 to solve for [tex]\(x\)[/tex]:

[tex]\[ x = \frac{3.75}{3} = 1.25 \][/tex]

Therefore, the solution to the system of equations is:

[tex]\[ y = 0.5625 \quad \text{and} \quad x = 1.25 \][/tex]

So, the point [tex]\((x, y)\)[/tex] that satisfies both equations is:

[tex]\[ (x, y) = (1.25, 0.5625) \][/tex]
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