At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To solve the system of equations given by:
[tex]\[ \begin{array}{l} 7x - 4y = -8 \\ y = \frac{3}{4}x - 3 \end{array} \][/tex]
we follow these steps:
1. Substitute the expression for [tex]\(y\)[/tex] from the second equation into the first equation:
The second equation gives [tex]\( y = \frac{3}{4}x - 3 \)[/tex].
Substitute [tex]\( y = \frac{3}{4}x - 3 \)[/tex] into the first equation:
[tex]\[ 7x - 4\left( \frac{3}{4}x - 3 \right) = -8 \][/tex]
2. Simplify the equation:
Distribute [tex]\( -4 \)[/tex] across the terms inside the parentheses:
[tex]\[ 7x - 4 \cdot \frac{3}{4}x + 4 \cdot 3 = -8 \][/tex]
This simplifies to:
[tex]\[ 7x - 3x + 12 = -8 \][/tex]
Combine like terms:
[tex]\[ 4x + 12 = -8 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Isolate [tex]\( x \)[/tex] by first subtracting 12 from both sides:
[tex]\[ 4x = -8 - 12 \][/tex]
[tex]\[ 4x = -20 \][/tex]
Divide both sides by 4:
[tex]\[ x = -5 \][/tex]
4. Substitute [tex]\( x \)[/tex] back into the second original equation to find [tex]\( y \)[/tex]:
Use the second equation [tex]\( y = \frac{3}{4}x - 3 \)[/tex]:
[tex]\[ y = \frac{3}{4}(-5) - 3 \][/tex]
Multiply:
[tex]\[ y = -\frac{15}{4} - 3 \][/tex]
Convert [tex]\(-3\)[/tex] to quarters:
[tex]\[ y = -\frac{15}{4} - \frac{12}{4} \][/tex]
Add the fractions:
[tex]\[ y = -\frac{27}{4} \][/tex]
Convert [tex]\(-\frac{27}{4}\)[/tex] to a decimal:
[tex]\[ y = -6.75 \][/tex]
Therefore, the solution to the system of equations is approximately:
[tex]\[ (x, y) = (-5.0, -6.75) \][/tex]
This is the point where the two equations intersect on the graph.
[tex]\[ \begin{array}{l} 7x - 4y = -8 \\ y = \frac{3}{4}x - 3 \end{array} \][/tex]
we follow these steps:
1. Substitute the expression for [tex]\(y\)[/tex] from the second equation into the first equation:
The second equation gives [tex]\( y = \frac{3}{4}x - 3 \)[/tex].
Substitute [tex]\( y = \frac{3}{4}x - 3 \)[/tex] into the first equation:
[tex]\[ 7x - 4\left( \frac{3}{4}x - 3 \right) = -8 \][/tex]
2. Simplify the equation:
Distribute [tex]\( -4 \)[/tex] across the terms inside the parentheses:
[tex]\[ 7x - 4 \cdot \frac{3}{4}x + 4 \cdot 3 = -8 \][/tex]
This simplifies to:
[tex]\[ 7x - 3x + 12 = -8 \][/tex]
Combine like terms:
[tex]\[ 4x + 12 = -8 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Isolate [tex]\( x \)[/tex] by first subtracting 12 from both sides:
[tex]\[ 4x = -8 - 12 \][/tex]
[tex]\[ 4x = -20 \][/tex]
Divide both sides by 4:
[tex]\[ x = -5 \][/tex]
4. Substitute [tex]\( x \)[/tex] back into the second original equation to find [tex]\( y \)[/tex]:
Use the second equation [tex]\( y = \frac{3}{4}x - 3 \)[/tex]:
[tex]\[ y = \frac{3}{4}(-5) - 3 \][/tex]
Multiply:
[tex]\[ y = -\frac{15}{4} - 3 \][/tex]
Convert [tex]\(-3\)[/tex] to quarters:
[tex]\[ y = -\frac{15}{4} - \frac{12}{4} \][/tex]
Add the fractions:
[tex]\[ y = -\frac{27}{4} \][/tex]
Convert [tex]\(-\frac{27}{4}\)[/tex] to a decimal:
[tex]\[ y = -6.75 \][/tex]
Therefore, the solution to the system of equations is approximately:
[tex]\[ (x, y) = (-5.0, -6.75) \][/tex]
This is the point where the two equations intersect on the graph.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.