determine the resulting equation if one variable is solved in terms of the other variable in one equation and substitute this variable in the other equation.
1.) 2x+5y=9
-x+y=2
2.) 3x+y=2
9x+2y=7
3.) x-y=-3
3x +y=19
#1 We see that x = y-2, so
2(y-2)+5y = 9
Do the others in like wise.
To determine the resulting equation by solving one variable in terms of the other and substituting it into the other equation, follow these steps:
1.) Write down the given system of equations:
1.) 2x + 5y = 9
-x + y = 2
2.) 3x + y = 2
9x + 2y = 7
3.) x - y = -3
3x + y = 19
2.) Solve one equation for one variable in terms of the other variable:
1.) To solve for x in terms of y in the first equation, we isolate x by adding x to both sides of the equation:
-x + y = 2
-x = 2 - y
x = -2 + y
2.) To solve for y in terms of x in the second equation, we isolate y by subtracting 3x from both sides of the equation:
3x + y = 2
y = 2 - 3x
3.) To solve for x in terms of y in the third equation, we isolate x by adding y to both sides of the equation:
x - y = -3
x = -3 + y
3.) Substitute the solved variable into the other equation:
1.) Substitute x = -2 + y into the second equation:
2x + 5y = 9
2(-2 + y) + 5y = 9
-4 + 2y + 5y = 9
7y - 4 = 9
7y = 9 + 4
7y = 13
y = 13/7
Substitute y = 13/7 into x = -2 + y:
x = -2 + (13/7)
x = (-14 + 13)/7
x = -1/7
Therefore, the resulting equation is x = -1/7 and y = 13/7.
2.) Substitute y = 2 - 3x into the second equation:
9x + 2y = 7
9x + 2(2 - 3x) = 7
9x + 4 - 6x = 7
3x + 4 = 7
3x = 7 - 4
3x = 3
x = 1
Substitute x = 1 into y = 2 - 3x:
y = 2 - 3(1)
y = 2 - 3
y = -1
Therefore, the resulting equation is x = 1 and y = -1.
3.) Substitute x = -3 + y into the second equation:
3x + y = 19
3(-3 + y) + y = 19
-9 + 3y + y = 19
4y - 9 = 19
4y = 19 + 9
4y = 28
y = 28/4
y = 7
Substitute y = 7 into x = -3 + y:
x = -3 + 7
x = 4
Therefore, the resulting equation is x = 4 and y = 7.