# Solve the following simultaneous equations. 3a+5b=26, a+5b=22

Question
Systems of equations
Solve the following simultaneous equations. 3a+5b=26, a+5b=22

2021-01-31
When solving a system of equations, use the elimination method or the substitution method.
Since the second equation can be easily solved for aa, the substitution method is the most appropriate method for this system.
Solving a+5b=22 for aa gives a=22−5b.
Now, substitute a=22−5b into the first equation of 3a+5b=26 and solve for b:
3a+5b=26 3(22-5b)+5b=26 66-15b+5b=26 66-10b=26 -10b=-40 b=4
To find aa, substitute b=4 into a=22−5b. This gives a=22−5(4)=2.
The solution of the system is then (a,b)=(2,4).
To find aa, substitute b=4b=4 into a=22−5b. This gives a=22−5(4)=2.
The solution of the system is then (a,b)=(2,4).

### Relevant Questions

Show the following simultaneous equations in matrix form:
$$4x-4y-6=0$$
$$16y=14x+4$$

a) Convert the following equations into matrix:
$$\displaystyle{x}–{y}={3}$$
$$\displaystyle{2}{x}+{3}{y}={1}$$
A roadside vegetable stand sells pumpkins for $5 each and squashes for$3 each. One day they sold 6 more squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many pumpkins and quash they sold? asked 2021-03-06 Write and solve a system of equations for each situation. Check your answers A shop has one-pound bags of peanuts for$2 and three-pound bags of peanuts for $5.50. If you buy 5 bags and spend$17, how many of each size bag did you buy?
Solve the system of equations. {(x,+,4y,=,-2),(-2x,+12y,=,9):}
Please, solve the system of equations: {(5x,+,y,=,14),(2x,+,y,=,5):}
What are the solutions to the following system of equations?
$$y = x^{2} + 3x − 7$$
$$3x − y = −2$$

Use back-substitution to solve the system of linear equations.
$$\begin{cases}x &-y &+5z&=26\\ &\ \ \ y &+2z &=1 \\ & &\ \ \ \ \ z & =6\end{cases}$$
(x,y,z)=()