Find the solution to the system by the substitution method.

3x – 5y = 7

x – 4y = -7

3x – 5y = 7

x – 4y = -7

3x - 5y = 7

x - 4y = -7

x = 4y - 7 {added 4y to each side of bottom equation}

3(4y - 7) - 5y = 7 {substituted (4y - 7), in for x, into top equation}

12y - 21 - 5y = 7 {used distributive property}

7y - 21 = 7 {combined like terms}

7y = 28 {added 21 to each side}

y = 4 {divided each side by 7}

x = 4y - 7 {new bottom equation}

x = 4(4) - 7 {substituted 4, in for y, into new bottom equation}

x = 16 - 7 {multiplied}

x = 9 {subtracted}

By the way, that means the point (9,4) is the point of intersection

of the two lines when they are graphed on a coordinate plane.

x - 4y = -7

x = 4y - 7 {added 4y to each side of bottom equation}

3(4y - 7) - 5y = 7 {substituted (4y - 7), in for x, into top equation}

12y - 21 - 5y = 7 {used distributive property}

7y - 21 = 7 {combined like terms}

7y = 28 {added 21 to each side}

y = 4 {divided each side by 7}

x = 4y - 7 {new bottom equation}

x = 4(4) - 7 {substituted 4, in for y, into new bottom equation}

x = 16 - 7 {multiplied}

x = 9 {subtracted}

**x = 9 and y = 4**By the way, that means the point (9,4) is the point of intersection

of the two lines when they are graphed on a coordinate plane.

*- Algebra House*