Solve the system of equations
−9x+7y=8
−6x+4y=2
To solve for y, multiply all the terms of each equation so that the coefficients of x are the same
1) Multiply all the terms of the first equation by -2
After you have multiplied, you will get this:
18x - 14y = - 16
2) Multiply all the terms of the second equation by +3
After you have multiplied, you will get this:
-18x + 12y = 6
3) Combine the equations to let the x terms go to zero
color(white)(m)18x - 14y = - 16
-18x + 12y = 6
color(white)()―――――――――――
color(white)(mm)color(lightgray)0 - 2y =-10
4) Divide both sides by -2 to isolate y
y = 5 larr answer for y
color(white)(mmm)―――――――――――
To solve for x, sub in the value of y
1) Sub in 5 in the place of y in one of the original equations
−9x+7 y =8
−9x+7(5)=8
2) Clear the parentheses
-9x + 35 = 8
3) Subtract 35 from both sides to isolate the -9x term
-9x = - 27
4) Divide both sides by -9 to isolate x
x = 3 larr answer for x
color(white)(mmm)―――――――――――
Check
Sub the values for x and y into the original equations
−9 x +7 y=8
-9(3) + 7(5) should equal 8
color(white)(.)-27 + 35 should equal 8
8 does equal 8 ✓
color(white)()―――――――――――
−6 x +4 y=2
-6(3) + 4(5) should equal 2
color(white)(.)-18 + 20 should equal 2
2 does equal 2 ✓
Check
