odveza6ad

2023-03-06

How to solve the system of equations $3x+2y=14$ and $y=x+2$ by substitution?

Metafune7re

Beginner2023-03-07Added 2 answers

We can substitute (x + 2) for y in the first equation and solve for x since the second equation has already been solved for y:

$3x+2y=14$ becomes:

$3x+2(x+2)=14$

$3x+(2\times x)+(2\times 2)=14$

$3x+2x+4=14$

$(3+2)x+4=14$

$5x+4=14$

$5x+4-{4}=14-{4}$

$5x+0=10$

$5x=10$

$\frac{5x}{{5}}=\frac{10}{{5}}$

$\frac{{\overline{){5}}}x}{\overline{){5}}}=2$

$x=2$

Substitute 2 for x in the second solution and solve for y:

$y=x+2$ becomes:

$y=2+2$

$y=4$

The Solution Is: x = 2 and y = 4 or (2, 4)

$3x+2y=14$ becomes:

$3x+2(x+2)=14$

$3x+(2\times x)+(2\times 2)=14$

$3x+2x+4=14$

$(3+2)x+4=14$

$5x+4=14$

$5x+4-{4}=14-{4}$

$5x+0=10$

$5x=10$

$\frac{5x}{{5}}=\frac{10}{{5}}$

$\frac{{\overline{){5}}}x}{\overline{){5}}}=2$

$x=2$

Substitute 2 for x in the second solution and solve for y:

$y=x+2$ becomes:

$y=2+2$

$y=4$

The Solution Is: x = 2 and y = 4 or (2, 4)