Answer:
x = 4 , y = 4
Step-by-step explanation:
Solve the following system:
{4 x - 2 y = 8 | (equation 1)
y = (3 x)/2 - 2 | (equation 2)
Express the system in standard form:
{4 x - 2 y = 8 | (equation 1)
-(3 x)/2 + y = -2 | (equation 2)
Add 3/8 × (equation 1) to equation 2:
{4 x - 2 y = 8 | (equation 1)
0 x+y/4 = 1 | (equation 2)
Divide equation 1 by 2:
{2 x - y = 4 | (equation 1)
0 x+y/4 = 1 | (equation 2)
Multiply equation 2 by 4:
{2 x - y = 4 | (equation 1)
0 x+y = 4 | (equation 2)
Add equation 2 to equation 1:
{2 x+0 y = 8 | (equation 1)
0 x+y = 4 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 4 | (equation 1)
0 x+y = 4 | (equation 2)
Collect results:
Answer: {x = 4 , y = 4
The solutions to the equations [tex]4x-2y=8[/tex] and [tex]y=\frac{3}{2} x-2[/tex] are [tex]x=4[/tex] and [tex]y=4[/tex] .
Equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
We have,
[tex]4x-2y=8[/tex] [tex]........(i)[/tex]
[tex]y=\frac{3}{2} x-2[/tex] [tex]........(ii)[/tex]
Now,
First rewrite and simplify equation [tex](ii)[/tex] ;
[tex]3x-2y=4[/tex] [tex]........(iii)[/tex]
Now, subtract equation [tex](iii)[/tex] from equation [tex](i)[/tex];
We get,
[tex]x=4[/tex],
Now, substitute this value of [tex]x[/tex] in equation [tex](ii)[/tex];
[tex]y=\frac{3}{2} *\ 4-2[/tex]
[tex]y=6-2[/tex]
[tex]y=4[/tex]
So, the solutions of given equations are [tex]x=4[/tex] and [tex]y=4[/tex] , which are find out using the elimination method.
Hence, we can say that the solutions to the equations [tex]4x-2y=8[/tex] and [tex]y=\frac{3}{2} x-2[/tex] are [tex]x=4[/tex] and [tex]y=4[/tex] .
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