Ask question

# Using substitution method solve 3x+4y=7 2x-3y=-1 # Using substitution method solve 3x+4y=7 2x-3y=-1

Question
Linear equations and graphs asked 2021-02-11
Using substitution method solve
$$\displaystyle{3}{x}+{4}{y}={7}$$
$$\displaystyle{2}{x}-{3}{y}=-{1}$$

## Answers (1) 2021-02-12
From the second equation, $$\displaystyle{2}{x}={3}{y}-{1}$$, so $$\displaystyle{x}=\frac{{{3}{y}-{1}}}{{2}}.$$
Substitute for x in the first equation:
$$\displaystyle{3}\frac{{{3}{y}-{1}}}{{2}}+{4}{y}={7}$$, multiply each side by 2:
$$\displaystyle{3}{\left({3}{y}-{1}\right)}+{8}{y}={14},{9}{y}-{3}+{8}{y}={14},{17}{y}={17},{y}={1},$$ therefore $$\displaystyle{x}=\frac{{{3}-{1}}}{{2}}=\frac{{2}}{{2}}={1}$$.
Solution: x=1, y=1.

### Relevant Questions asked 2021-04-02
Solve the system of equations using the addition/elimination method.
4x+3y=15
2x-5y=1 asked 2021-02-22
To solve: The system of congruence $$\displaystyle{x}={2}{\left({b}\text{mod}{3}\right)},{x}={1}{\left({b}\text{mod}{4}\right)},\ {\quad\text{and}\quad}\ {x}={3}{\left({b}\text{mod}{5}\right)}$$ using the method of back substitution. asked 2021-01-31
Simplify each expression.
1. -n+9n+3-8-8n
2. 3(-4x+5y)-3x(2+4)
5. 5-4y+x+9y
7. -2x+3y-5x-(-8y) asked 2021-05-19
The method of undetermined coefficients can sometimes be used to solve first-order ordinary differential equations. Use the method to solve the following equations.
$$y'-3y=5e^{3x}$$ asked 2021-02-11

Solve the following system of linear equations in two variables by Substitution method.
$$5x-2y=-7$$
$$x=-2y+1$$ asked 2021-03-29
Solve the system. If the system does not have one unique solution, also state whether the system is onconsistent or whether the equations are dependent.
2x-y+z=-3
x-3y=2
x+2y+z=-7 asked 2021-05-30
Verify the factorization using the FOIL method.
$$(x+3y)(x-7y)=x^{2}-7xy+3xy-21y^{2}=x^{2}-4xy-21y^{2}$$ asked 2021-02-13
Solve the system of linear equations using matrices.
x+y+z=3
2x+3y+2z=7
3x-4y+z=4 asked 2020-11-11
Describe a method you could use to find the value of x in the figure at the right without using a protractor. asked 2021-06-08
Solve the higher order derivatives:
y''+4y+3y=0
...