How do you solve #2x+5y=11# and #4x+3y=1# using substitution?

Question

Avery Alexander · Accepted Answer

#y=3,x=-2# We have #2x=11-5y# Multiplying both sides by #2#,we get #4x=22-10y# substituting this value in #2#nd equation,we have, #22-10y=1-3y# Or,#21=7y# Thus,we get, #y=3# and substituting this value in first equation we get #x# as #-2#

Jameson Allen · Answer

undefined 1. Solve the first equation for x or y.
2. Substitute the expression from step 1 into the other equation.
3. Solve the resulting equation for the variable.
4. Substitute the value found in step 3 back into the equation from step 1 to find the other variable.

Savannah Anderson · Answer

undefined To solve the system of equations $2x + 5y = 11$ and $4x + 3y = 1$ using substitution:

1. Solve one of the equations for one variable in terms of the other.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 into either of the original equations to solve for the other variable.
5. Verify the solution by checking it in both original equations.

Step-by-step:

1. Solve the first equation $2x + 5y = 11$ for $x$:
$$2x = 11 - 5y$$
$$x = \frac{11}{2} - \frac{5}{2}y$$

2. Substitute $x = \frac{11}{2} - \frac{5}{2}y$ into the second equation $4x + 3y = 1$:
$$4\left(\frac{11}{2} - \frac{5}{2}y\right) + 3y = 1$$

3. Solve for $y$:
$$22 - 10y + 3y = 1$$
$$22 - 7y = 1$$
$$-7y = 1 - 22$$
$$-7y = -21$$
$$y = 3$$

4. Substitute $y = 3$ into $x = \frac{11}{2} - \frac{5}{2}y$:
$$x = \frac{11}{2} - \frac{5}{2}(3)$$
$$x = \frac{11}{2} - \frac{15}{2}$$
$$x = -2$$

5. Verify the solution by checking it in both original equations:
$$2(-2) + 5(3) = 11$$
$$4(-2) + 3(3) = 1$$

Both equations are satisfied by $x = -2$ and $y = 3$, so the solution is correct.