Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To solve the system of equations
[tex]\[ \begin{cases} 6x + 5y = 88 \\ 5x + 6y = 88 \end{cases} \][/tex]
we'll use the method of elimination. Here's a step-by-step solution:
1. Label the equations:
[tex]\[ \begin{aligned} \text{Equation 1:} & \quad 6x + 5y = 88 \\ \text{Equation 2:} & \quad 5x + 6y = 88 \end{aligned} \][/tex]
2. Multiply Equation 1 by 5 and Equation 2 by 6 to make the coefficients of [tex]\(x\)[/tex] in both equations the same:
[tex]\[ \begin{aligned} 30x + 25y &= 440 \quad \text{(Equation 1 multiplied by 5)} \\ 30x + 36y &= 528 \quad \text{(Equation 2 multiplied by 6)} \end{aligned} \][/tex]
3. Subtract the first modified equation from the second modified equation to eliminate [tex]\(x\)[/tex]:
[tex]\[ (30x + 36y) - (30x + 25y) = 528 - 440 \][/tex]
Simplifying this, we get:
[tex]\[ 30x + 36y - 30x - 25y = 88 \][/tex]
Simplifying further:
[tex]\[ 11y = 88 \][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{88}{11} = 8 \][/tex]
5. Substitute [tex]\(y = 8\)[/tex] back into one of the original equations to solve for [tex]\(x\)[/tex]:
Using Equation 1:
[tex]\[ 6x + 5(8) = 88 \][/tex]
Simplifying:
[tex]\[ 6x + 40 = 88 \][/tex]
[tex]\[ 6x = 88 - 40 \][/tex]
[tex]\[ 6x = 48 \][/tex]
[tex]\[ x = \frac{48}{6} = 8 \][/tex]
6. Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (8, 8) \][/tex]
So, the solution to the system of equations is [tex]\((8, 8)\)[/tex].
[tex]\[ \begin{cases} 6x + 5y = 88 \\ 5x + 6y = 88 \end{cases} \][/tex]
we'll use the method of elimination. Here's a step-by-step solution:
1. Label the equations:
[tex]\[ \begin{aligned} \text{Equation 1:} & \quad 6x + 5y = 88 \\ \text{Equation 2:} & \quad 5x + 6y = 88 \end{aligned} \][/tex]
2. Multiply Equation 1 by 5 and Equation 2 by 6 to make the coefficients of [tex]\(x\)[/tex] in both equations the same:
[tex]\[ \begin{aligned} 30x + 25y &= 440 \quad \text{(Equation 1 multiplied by 5)} \\ 30x + 36y &= 528 \quad \text{(Equation 2 multiplied by 6)} \end{aligned} \][/tex]
3. Subtract the first modified equation from the second modified equation to eliminate [tex]\(x\)[/tex]:
[tex]\[ (30x + 36y) - (30x + 25y) = 528 - 440 \][/tex]
Simplifying this, we get:
[tex]\[ 30x + 36y - 30x - 25y = 88 \][/tex]
Simplifying further:
[tex]\[ 11y = 88 \][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{88}{11} = 8 \][/tex]
5. Substitute [tex]\(y = 8\)[/tex] back into one of the original equations to solve for [tex]\(x\)[/tex]:
Using Equation 1:
[tex]\[ 6x + 5(8) = 88 \][/tex]
Simplifying:
[tex]\[ 6x + 40 = 88 \][/tex]
[tex]\[ 6x = 88 - 40 \][/tex]
[tex]\[ 6x = 48 \][/tex]
[tex]\[ x = \frac{48}{6} = 8 \][/tex]
6. Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (8, 8) \][/tex]
So, the solution to the system of equations is [tex]\((8, 8)\)[/tex].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.