2) 2x + 3y= 11 -x-5y=-23
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The solution to given system of equations y = 3x - 9 and y = -2x + 16 are (x, y) = (5, 6)
The solution to given system of equations y = 5x + 22 and -6x - 4y = -10 are (x, y) = (-3, 7)
<em><u>Solution:</u></em>
Given that, we have to solve each system by substitution method
<em><u>Given system of equations are:</u></em>
y = 3x - 9 ----------- eqn 1
y = -2x + 16 -------- eqn 2
Substitution method is done by substituting eqn 2 in eqn 1
<em><u>Substitute the value of "y" from eqn 2 into eqn 1</u></em>
-2x + 16 = 3x - 9
Move the variables to one side and constants to other side
-2x - 3x = -9 - 16
Combine the like terms
-5x = -25
Cancel the negative sign on both sides of equation
5x = 25
<em><u>Substitute x = 5 in eqn 1</u></em>
y = 3(5) - 9
y = 15 - 9
<h3>y = 6</h3>Thus solution to given system of equations are (x, y) = (5, 6)
<em><u>Given another system of equations are:</u></em>
y = 5x + 22 ----- eqn 1
-6x - 4y = -10 ------ eqn 2
Substitute eqn 1 in eqn 2
-6x - 4(5x + 22) = -10
-6x - 20x - 88 = -10
Move the variables to one side and constants to other side
-26x = -10 + 88
-26x = 78
<h3>x = -3</h3>Substitute x = -3 in eqn 1
y = 5( - 3) + 22
y = -15 + 22
<h3>y = 7</h3>Thus solution to given system of equations are (x, y) = (-3, 7)