Solve by elimination ([-7y+5x-11=0],[3y+20 x-44=0]:}

Question

Bytelearn · Accepted Answer

Write Equations: First, let's write down the system of equations to be solved by elimination: $$ \begin{align*} -7y + 5x - 11 &= 0 \ 3y + 20x - 44 &= 0 \end{align*} $$ We want to eliminate one of the variables by combining the equations. To do this, we need to make the coefficients of one of the variables (either x or y) the same or opposites in both equations.Multiply Equations: Let's choose to eliminate the y variable. To do this, we need to multiply the first equation by 3 and the second equation by 7 so that the coefficients of y in both equations are opposites. $$ \begin{align*} 3(-7y + 5x - 11) &= 3(0) \ 7(3y + 20x - 44) &= 7(0) \end{align*} $$Perform Multiplication: Now, let's perform the multiplication: $$ \begin{align*} -21y + 15x - 33 &= 0 \ 21y + 140x - 308 &= 0 \end{align*} $$Eliminate y: Next, we add the two equations together to eliminate y: $$ (-21y + 15x - 33) + (21y + 140x - 308) = 0 + 0 $$Add Equations: After adding the equations, we get: $$ 15x + 140x - 33 - 308 = 0 $$Combine Terms: Combining like terms gives us: $$ 155x - 341 = 0 $$Solve for x: Now, we solve for x by adding 341 to both sides of the equation: $$ 155x = 341 $$Divide by 155: Next, we divide both sides by 155 to find the value of x: $$ x = \frac{341}{155} $$Substitute into Equation: Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation: $$ -7y + 5\left(\frac{341}{155}\right) - 11 = 0 $$Multiply 5: We multiply 5 by $\frac{341}{155}$ to get: $$ -7y + \frac{1705}{155} - 11 = 0 $$Convert 11: Next, we convert 11 to a fraction with the same denominator to combine it with $\frac{1705}{155}$: $$ -7y + \frac{1705}{155} - \frac{1705}{155} = 0 $$

Solve by elimination $\newline$ \begin{array} -7 y+5 x-11=0 \\ 3 y+20 x-44=0 \end{array}.

Full solution

More problems from Solve a system of equations using elimination

Related topics

Solve by elimination\newline \begin{array} -7 y+5 x-11=0 \\ 3 y+20 x-44=0 \end{array}.

Solve by elimination $\newline$ \begin{array} -7 y+5 x-11=0 \\ 3 y+20 x-44=0 \end{array}.